front page master - Unit

Faculty of Science and Technology

MASTER’S THESIS

Study program/ Specialization:

Engineering Structures and Materials - Civil engineering structures

Spring semester, 2018

Open / Restricted access

Writer:

Thomas Ødegaard

………………………………………… (Writer’s signature)

Faculty supervisor:

Samindi Samarakoon

External supervisor(s):

Jan Fredrik Rambech

Title of thesis:

Seismic performance assessment of reinforced concrete structures: a case study of Kanti Children’s Hospital, Kathmandu, Nepal

Credits (ECTS): 30

Key words: Performance based seismic design

Eurocode 8

IS-1893 Time-history analysis

Pushover analysis

Pages: 120

+ enclosure: 43

Stavanger, 15-6-2018

Date/year

Front page for master thesis

Faculty of Science and Technology

University of Stavanger Abstract

Thomas Ødegaard 2

ABSTRACT

Structures should be ensured good structural performance in the event of high magnitude earthquakes. This

thesis is built around a case study of Kanti Children’s Hospital, Kathmandu, Nepal where there is a history

of high magnitude earthquakes. A seismic performance assessment was performed for the structural system

of Kanti Children’s Hospital as a measure of quality assurance.

The theory chapter of thesis will provide the underlying theory for seismic hazards, structural modelling

and analysis, and seismic code applications.

For the structural analyses of the case study, a combination of linear (lateral force, response spectrum and

modal time-history) and nonlinear (pushover and direct integration time history) analyses were performed.

While the structural design of the case study complies with the Indian seismic code (IS1893), with a few

limitations, the difference is seismic demand compared to the European seismic code (EC8) is substantial.

The structure is not expected to comply with the criteria of Eurocode 8.

The performance assessment was conducted after a performance based seismic design approach, with

acceptance criteria from FEMA 356 and ASCE 41-13. The structure was subjected to seismic loading

equivalent of earthquakes with 50%-, 10%- and 2% probability of occurrence in 50 years. The following

results were obtained:

Operational

(O)

Immediate

Occupancy

(IO)

Life Safety

(LS)

Near Collapse

(NC)

50% / 50 years

10% / 50 years

2% / 50 years

The stairway tower is considered to be the weak-point of the structure. To increase the performance the

focus should be put into reducing the overall torsional irregularity and strengthening the stairway.

University of Stavanger Acknowledgements

Thomas Ødegaard 3

ACKNOWLEDGEMENTS

“There is no such thing as a ‘self-made man. We are made up of thousands of others. Everyone

who has ever done a kind deed for us, or spoken one word of encouragement to us, has entered

into the make-up of our character and of our thoughts, as well as our success.”

- George Matthew Adams

First and foremost, I would like to thank Anne Asselin at Engineers Without Borders for providing

the subject of the thesis, coordinating the supervision, and for making the field in Nepal visit a

possibility. For the technical part of thesis, I would like to thank my school supervisor, Samindi

Samrakoon, and my supervisor at Norconsult, Jan Fredrik Rambech. Lastly, my wife Enya

deserves a huge thanks for coping with through all of my studies.

University of Stavanger Nomenclature

Thomas Ødegaard 4

NOMENCLATURE

Latin letters

Chapter 2

𝑴𝑾 Moment magnitude

𝑴𝒔 Surface wave magnitude

P-∆ Second order effect

Chapter 3

M Mass matrix

C Damping matrix

K Stiffness matrix

𝒖 Displacement

�̇� Velocity

�̈� Acceleration

𝝎 Mode of vibration

𝜻 Damping ratio

𝒆𝟎 Accidental eccentricity

r Torsional radius

ls Radius of gyration

𝛀 Diagonal matrix of eigenvectors

𝚽 Mode-shape

Chapter 4

I Importance factor (EC8 and IS1893)

q Behavior factor (EC8)

R Behvaior factor (IS1893)

𝜶𝒖/𝜶𝟏 Overstrength factor (EC8)

𝑻 Period of vibration

University of Stavanger Nomenclature

Thomas Ødegaard 5

Abbreviations

OMRF Ordinary Moment Resisting Frame (IS1893)

SMRF Special Moment Resisting Frame (IS1893)

PGA Peak ground acceleration

EC8 Eurocode 8

FEMA Federal Emergency Management Agency

ASCE American Society of Civil Engineers

PSHA Probabilistic Seismic Hazard Analysis

DSHA Deterministic Seismic Hazard Analysis

NL Nonlinear

L Linear

SDOF Single degree of freedom

MDOF Multiple degree of freedom

HHT Hilber-Hughes-Taylor

FEM Finite Element Method

SPT Standard Penetration Test (Geotechnical)

SSI Soil-Structure-Interaction

DCH – DCM – DCL Ductility Class High – Medium – Low

SRSS Square Root of sum of squares

CQC Complete Quadradic Combination

FNA Fast Nonlinear Analysis (Nonlinear Modal Time-History)

Mumty Stairway-tower

University of Stavanger Contents

Thomas Ødegaard 6

CONTENTS

Abstract ................................................................................................................................. 2

Acknowledgements .............................................................................................................. 3

Nomenclature ....................................................................................................................... 4

Contents ................................................................................................................................ 6

List of figures ........................................................................................................................ 8

List of tables........................................................................................................................ 11

1 Introduction ................................................................................................................... 13

1.1 Background ......................................................................................................................................... 13 1.2 Problem formulation........................................................................................................................... 13 1.3 Limitations ........................................................................................................................................... 13 1.4 Structure of the report ........................................................................................................................ 14

2 Seismic Hazard .............................................................................................................. 15

2.1 Earthquakes......................................................................................................................................... 15 2.2 Faults .................................................................................................................................................... 16 2.3 Classification of earthquakes ............................................................................................................. 17 2.4 Seismic Hazard Assessment ............................................................................................................... 19 2.5 Seismicity in Nepal .............................................................................................................................. 20

3 Structural modelling and analysis ............................................................................... 22

3.1 Structural analysis elements .............................................................................................................. 22 3.2 Diaphragm ........................................................................................................................................... 23 3.3 Nonlinear behavior ............................................................................................................................. 24 3.4 Damping ............................................................................................................................................... 28 3.5 Torsion ................................................................................................................................................. 30 3.6 Modal ................................................................................................................................................... 31 3.7 Response spectrum analysis ............................................................................................................... 32 3.8 Nonlinear static analysis ..................................................................................................................... 33 3.9 Time History Analysis .......................................................................................................................... 34

4 Analysis and design guidelines to evaluate seismic action ......................................... 36

4.1 Eurocode 8-1 ........................................................................................................................................ 36 4.2 IS1893 ................................................................................................................................................... 48 4.3 NBC 105 ............................................................................................................................................... 52 4.4 Performance based seismic design ..................................................................................................... 54

5 Case Study ...................................................................................................................... 58

5.1 Structural analysis Model .................................................................................................................. 61 5.2 EC8 ....................................................................................................................................................... 67 5.3 IS1893 ................................................................................................................................................... 80 5.4 Time History Analysis ........................................................................................................................ 86 5.5 Pushover Analysis ............................................................................................................................. 100 5.6 Seismic performance assessment ..................................................................................................... 103

6 Discussion ..................................................................................................................... 108

6.1 Uncertainties in modelling and analysis .......................................................................................... 108 6.2 Code comparison ............................................................................................................................... 111 6.3 Case Study ......................................................................................................................................... 114

7 Conclusion .................................................................................................................... 121

University of Stavanger Contents

Thomas Ødegaard 7

Appendix A – Architectural drawings of Kanti Children’s hospital .......................... 124

Appendix B – Flowcharts ................................................................................................ 126

B-1: Linear elastic analysis flowchart ............................................................................ 126

B-2: Pushover analysis flowchart ................................................................................... 127

B-3: Time-history analysis flowchart ............................................................................. 128

Appendix C – N2-Pushover Procedure .......................................................................... 129

C-1: Eurocode 8: .............................................................................................................. 129

C-2: Performance assessment using N2-Pushover procedure ..................................... 138

Appendix D – Analysis Results ....................................................................................... 146

D-1: Linear Modal Time History – 50% probability in 50 years ................................ 146

D-2: Nonlinear Modal Time History Analysis – 10% probability in 50 years ........... 149

D-3: Nonlinear Modal Time History Analysis – 2% probability in 50 years ............. 152

D-4: Nonlinear Direct Integration Time History – 10% probability in 50 years....... 155

D-5: Nonlinear Direct Integration Time History – 2% probability in 50 years......... 157

D-6: Gorkha Earthquake – Direct integration time history analysis ......................... 159

D-7: Hinge Performance – 10% in 50 years .................................................................. 160

D-8: Hinge Performance – 2% in 50 years .................................................................... 161

University of Stavanger

Thomas Ødegaard 8

LIST OF FIGURES

Figure 1-1 - Kanti Children’s Hospital - Ref. Team Consultants ................................................. 13

Figure 2-1 - Fault mechanisms (From Basic Earthquake Engineering [1]) ................................. 16

Figure 2-2 - Seismic waves (From Basic Earthquake Engineering [1]) ...................................... 16

Figure 2-3 - Seismic waves - speed and magnitude correlation (From USGS [3] ....................... 17

Figure 2-4 - Typical results of a PSHA (From Basic Earthquake Engineering [1]) .................... 19

Figure 2-5 - Comparison of PGA for Kathmandu city (Sunuwar 2005 [9]) ................................. 21

Figure 3-1 – Q4- and triangular shell elements in SAP2000 (From CSI Analysis Reference manual

[10]) ............................................................................................................................................... 23

Figure 3-2 - Comparison of meshing options effect on modal analysis ....................................... 23

Figure 3-3 - Diaphragm behavior (From CSI Analysis Reference manual [10]) ......................... 24

Figure 3-4 - Section material nonlinearity models (From Guidelines for Nonlinear Structural

Analysis for Design of Buildings [12]) .......................................................................................... 25

Figure 3-5 - Concentrated plastic hinges (From Guidelines for Nonlinear Structural Analysis for

Design of Buildings [12]) .............................................................................................................. 26

Figure 3-6 - Moment-curvature (y-,x-axis) relation for plastic hinges in SAP2000. L.S M3-hinge,

R.S P-M2-M3 Hinge ..................................................................................................................... 26

Figure 3-7 - Fiber type hinges - Conectrated plastic hinges (From Guidelines for Nonlinear

Structural Analysis for Design of Buildings [3]) .......................................................................... 27

Figure 3-8 - L.S Column section, R.S generated fiber hinge ........................................................ 27

Figure 3-9 - Shear wall model used in case study ........................................................................ 28

Figure 3-10 - Rayleigh damping (from Chopra [13]) ................................................................... 29

Figure 4-1 - Type 1 & 2 horizontal response spectrum, behavior factor not included ................. 37

Figure 4-2 - Design horizontal response spectrum ....................................................................... 41

Figure 4-3 - Bilinearization of the idealized pushover curve (From Annex B of EC8 [17]) ........ 43

Figure 4-4 - Pushover analysis - overstrength factor .................................................................... 46

Figure 4-5 - Seismic zone map of India (from IS1893 [5]) .......................................................... 48

Figure 4-6 - Design horizontal response spectrum for response spectrum analysis - IS1893 ...... 51

Figure 4-7 - Design horizontal response spectrum for lateral force method - IS1893.................. 51

Figure 4-8 - Seismic zones (NBC 105 [19]) ................................................................................. 52

Figure 4-9 - Design spectrum after NBC 105 [19] ....................................................................... 53

Figure 5-1 – North-elevation view (Ref. Team Consultants) ....................................................... 58

Figure 5-2 - Site plan, Kanti Children’s hospital .......................................................................... 58

Figure 5-3 – Beam- and column plan for story 1-4....................................................................... 58

Figure 5-4 - Shear wall configuration ........................................................................................... 59

Figure 5-5 - Structural analysis model .......................................................................................... 61

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Thomas Ødegaard 9

Figure 5-6 - Shear wall configuration ........................................................................................... 61

Figure 5-7 - Center of mass- and rigidity, and radius of gyration for main floors and mumty .... 62

Figure 5-8 - Diaphragm constrains. Left side. floor 1-roof, right side: mumty ............................ 63

Figure 5-9 - First four mode shapes in ascending order. Color-coding show resultant displacement.

....................................................................................................................................................... 65

Figure 5-10 - Location of nodes for calculation of inter-story drift. L.S Stairway, R.S. gravity

center ............................................................................................................................................. 66

Figure 5-11 - Design response spectrum - Eurocode 8 ................................................................. 72

Figure 5-12 - Interstory drifts at gravity center ............................................................................ 74

Figure 5-13 - Interstory drifts at stairway ..................................................................................... 74

Figure 5-14 -Pushover curve ......................................................................................................... 75

Figure 5-15 - Idealized pushover curves ....................................................................................... 76

Figure 5-16 - Target displacements in x-, y-direction .................................................................. 77

Figure 5-17 - Inter-story drifts at target displacements................................................................. 77

Figure 5-18 - Resultant displacements [mm] – Pushover X. l.s. “Damage limitation”, r.s. “No

collapse” ........................................................................................................................................ 78

Figure 5-19 - Resultant displacements [mm] – Pushover Y. l.s. “Damage limitation”, r.s. “No

collapse”. ....................................................................................................................................... 78

Figure 5-20 - Values for determination of over-strength factor.................................................... 79

Figure 5-21 - Evaluated nodes ...................................................................................................... 84

Figure 5-22 - Inter-story drifts, response spectrum analysis, IS1893 ........................................... 85

Figure 5-23 - Spectral acceleration of selected ground motions for 475- and 2475year return period

....................................................................................................................................................... 87

Figure 5-24 - Mean response +- SD for suite of ground motions ................................................. 87

Figure 5-25 - Mean response of three selected ground-motions for direct integration time-history

analysis .......................................................................................................................................... 87

Figure 5-26 - Applicability of ground motions for linear elastic analysis after Eurocode 8 ........ 89

Figure 5-27 - Interstory drifts with 50% probability of occurrence in 50 years ........................... 90

Figure 5-28 – Interstory drifts for FNA analysis with 10% probability of occurrence in 50 years

....................................................................................................................................................... 92

Figure 5-29 – Interstory drifts for FNA analysis with 2% probability of occurrence in 50 years 92

Figure 5-30 - Interstory drifts with 10% probability of occurrence in 50 years ........................... 94

Figure 5-31 - Applicability of ground motions for No collapse requirement after Eurocode 8 ... 95

Figure 5-32 - Interstory drifts with 2% probability of occurrence in 50 years ............................. 96

Figure 5-33 - Red dot: Kanti Path ground motion location. Blue dot: Kanti Childrens Hospital 97

Figure 5-34 - Spectral acceleration for Kanti Path ground motion ............................................... 97

Figure 5-35 - Kanti Path ground motions ..................................................................................... 98





Thomas Ødegaard 10

Figure 5-36 - Interstory drifts - Gorkha earthquake ...................................................................... 99

Figure 5-37 - Target displacements for seismic hazard levels .................................................... 100

Figure 5-38 - Interstory drift pushover analysis, with acceptance criteria.................................. 101

Figure 5-39 - Comparison of performance level for 50% of occurrence 50 years - hazard level

..................................................................................................................................................... 105


..................................................................................................................................................... 105


..................................................................................................................................................... 106

Figure 6-1 - Comparison of fiber-hinge result. L.S Direct integration, R.S. FNA ..................... 110

Figure 6-2 - Comparison of design seismic hazard for Kathmandu, Nepal ................................ 111

Figure 6-3 - Comparison of inter-story drifts - Response spectrum anlysis ............................... 114

Figure 6-4 - Proposed design change - slanted roof in stairway ................................................. 118

Figure 6-5 - Proposed design change - extend elevator shaft to stairway-roof ........................... 119

Figure 7-1 - Interstory drift at gravity center - 10% probability in 50 years .............................. 156

Figure 7-2 - Interstory drift at stairway - 10% probability in 50 years ....................................... 156

Figure 7-3 - Interstory drift at gravity center - 2% probability in 50 years ................................ 158

Figure 7-4 - Interstory drift at stairway - 2% probability in 50 years ......................................... 158


Thomas Ødegaard 11

LIST OF TABLES

Table 2-1 - Characteristics of seismic waves ................................................................................ 16

Table 2-2 - Comparison of MSK-64 and MMI classification ....................................................... 18

Table 2-3 - Earthquakes (>6.5Mw) in Nepal in the last century (From NCEI [8]) ...................... 20

Table 2-4 - PGA with probabilities of exceedance for Kathmandu, Nepal [9] ............................ 21

Table 3-1 - Nonlinear shear wall modelling ................................................................................. 28

Table 3-2 - Shear wall model used in case study .......................................................................... 28

Table 4-1 - Design ground accelerations correlated to return period ........................................... 36

Table 4-2 – equivalent SPT values for soil types.......................................................................... 38

Table 4-3 - Analysis models depending on structural regularity .................................................. 39

Table 4-4 - Initial behavior factor ................................................................................................. 40

Table 4-5 - Drift limits - Damage limitation ................................................................................. 47

Table 4-6 - Zone factors for IS1893 ............................................................................................. 48

Table 4-7 – equivalent SPT values for soil types.......................................................................... 49

Table 4-8 - PBSD after FEMA 356 with example acceptance criteria ......................................... 54

Table 4-9 - Approximation of performance levels of ASCE 41-13 and EC8-3 ........................... 54

Table 5-1 - Beam sections ............................................................................................................. 60

Table 5-2 - Column sections ......................................................................................................... 60

Table 5-3 - Slab sections ............................................................................................................... 60

Table 5-4 - Material properties ..................................................................................................... 62

Table 5-5 - Shear wall configuration ............................................................................................ 62

Table 5-6 - Torsional parameters .................................................................................................. 63

Table 5-7 - Modal mass participation ........................................................................................... 64

Table 5-8 - Changes to analysis model for nonlinear behavior .................................................... 66

Table 5-9 - Seismic design parameters - EC8 ............................................................................... 67

Table 5-10 – Characteristic loads - EC8 ....................................................................................... 67

Table 5-11 - Drift limits, Damage limitation ................................................................................ 68

Table 5-12 - Evaluation of torsional effect ................................................................................... 69

Table 5-13 - Cracked concrete stiffness ........................................................................................ 71

Table 5-14 - Initial response spectrum analysis ............................................................................ 71

Table 5-15 - Response spectrum analysis - modified behavior factor .......................................... 72

Table 5-16 - Drift limits - Damage limitation ............................................................................... 73

Table 5-17 - Displacement shape .................................................................................................. 76

Table 5-18 - Target displacements – Pushover analysis ............................................................... 76

Table 5-19 - Design values from pushover analysis ..................................................................... 78


Thomas Ødegaard 12

Table 5-20 - Calculated overstrength factor ................................................................................. 79

Table 5-21 - Seismic design parameters - IS1893 ........................................................................ 80

Table 5-22 - Loading scheme – IS1893 ........................................................................................ 80

Table 5-23 - Seismic weight after IS1893 .................................................................................... 81

Table 5-24 - Cracked concrete stiffness ........................................................................................ 81

Table 5-25 - Base shears - Lateral force method .......................................................................... 82

Table 5-26 - Design lateral loads - Lateral force method ............................................................. 82

Table 5-27 - Scaling of response spectrum ................................................................................... 83

Table 5-28 - Response spectrum analysis results ......................................................................... 83

Table 5-29 - Torsional irregularity................................................................................................ 84

Table 5-30 - Ground motion selection criteria .............................................................................. 86

Table 5-31 - Selected time histories .............................................................................................. 86

Table 5-32 - Base reactions for linear modal analysis .................................................................. 89

Table 5-33 - Base forces for the suite of ground motions ............................................................. 91

Table 5-34 - Base reactions with 10% probability of occurrence in 50 years .............................. 94

Table 5-35 - Hinge performance with 10% probability of occurrence in 50 years ...................... 94

Table 5-36 - Base reactions with 2% probability of occurrence in 50 years ................................ 95

Table 5-37 - Hinge performance with 2% probability of occurrence in 50 years ........................ 96

Table 5-38 - Base reactions from Gorkha earthquake analysis .................................................... 99

Table 5-39 - Hinge performance levels ...................................................................................... 102

Table 5-40 - Performance objective for Kanti Childrens Hospital ............................................. 103

Table 5-41 - Acceptance criteria ................................................................................................. 103

Table 5-42 - Comparison of base reaction for the different analysis methods ........................... 104

Table 5-43 - Performance assessment according to time-history analysis ................................. 107

Table 6-1 – Effective stiffness to model cracked moment of inertia .......................................... 112

Table 6-2 - Comparison of ground types .................................................................................... 112

Table 6-3 - Comparison of behavior factor for Eurocode 8 and IS1893 .................................... 113

Table 6-4 - Comparison of code-compliant design forces .......................................................... 114

Table 6-5 - Comparison of base reactions for linear elastic analyses - EC8 .............................. 115

Table 6-6 - Comparison of base reactions for nonlinear analyses - EC8 .................................... 115

Table 6-7 - Non-compliant criteria - IS1893 .............................................................................. 115

Table 6-8 - Modal mass participation ratio - Linear elastic analysis model ............................... 118

Table 7-1 - Performance level of Kanti Children’s hospital ....................................................... 121

Table 7-2 - Results from direct integration analysis with 10% probability of occurrence in 50 years

..................................................................................................................................................... 155


Thomas Ødegaard 13

1 INTRODUCTION

1.1 Background

The Norwegian non-profit organization FORUT is sponsoring an extension of Kanti Children’s

Hospital in Kathmandu, Nepal as shown in Figure 1-1. The building consists of four floors, with

a total height of 18.2 meters. Detailed drawings are found in Appendix A.

Through Engineers Without Borders (EWB), Norconsult has been involved to perform quality

assurance of the structural system. Furthermore, EWB provided the opportunity to have a master

thesis with a case study of Kanti Children’s Hospital, as an extended quality assurance.

The work in this thesis is thereby a collaboration between EWB, Norconsult, and FORUT, with

the aim of providing quality assurance of the structural performance for the structural system with

regards to seismic loading.

Figure 1-1 - Kanti Children’s Hospital - Ref. Team Consultants

1.2 Problem formulation

Is the structural design complying with the Indian Standard for seismic design (IS 1893), and how

does this compare to a seismic analysis after Eurocode 8? Regardless of code, what is the structural

performance be, e.g. is it possible to maintain operationality in the event of significant

earthquakes?

This thesis will provide insight to the process of seismic performance assessment of concrete

structures. With every step of the assessment, the underlying theory found relevant for structural

engineers to preform similar assessments is presented. It will also compare the different methods

given in standards to assess seismic performance.

1.3 Limitations

The theory of this thesis is limited to theory relevant for concrete structures. The reader is expected

to have basic knowledge of structural dynamics.

For the case study, the performance assessment is limited to displacement-based analyses

approaches. Individual structural members are therefore not evaluated, only the global structural

performance.


Thomas Ødegaard 14

1.4 Structure of the report

Chapter 2 – Seismic Hazard:

This chapter provides an overview of definitions relating to seismic hazards.

Chapter 3 – Structural modelling and analysis:

This chapter highlights the underlying theory of computational structural analysis, from modelling

to analysis

Chapter 4 – Code application

This chapter provides an overview the seismic codes relevant for case study. This includes

Eurocode 8, IS1839 (Indian code of seismic design), NBC105 (Nepali code of seismic design),

and highlight subjects of Performance Based Seismic Design with a basis in ASCE 41-13 and

FEMA 356.

Chapter 5 – Case specific structural analysis

This chapter presents the seismic analysis and results for the case study, with a focus on overall

structural performance. This includes analysis for Eurocode 8, IS1893, and structural performance

assessment with basis in ASCE 41-13 and FEMA 356.

Chapter 6 – Discussion

In this chapter the assumptions and uncertainties of the case study is highlighted, the differences

in seismic codes is evaluated, and the verdict of the seismic performance assessment of case study

discussed.

Chapter 7 – Conclusion

This chapter provides conclusions regarding code application of the case study, presents the final

results of the structural performance assessment, provides recommendations to improve seismic

performance of the case study, and suggests some measures to ensure good seismic performance

in future projects.


Thomas Ødegaard 15

2 SEISMIC HAZARD

This chapter aims to give a theoretical background for seismic hazards, and its application to

structural analysis and seismic design codes. It is in large parts based on theory from the book

Basic Earthquake Engineering [1].

2.1 Earthquakes

Earthquakes occur when energy stored in the earth’s crust is suddenly released. The main source

of earthquakes of significance originates from tectonic plate movement.

Figure 1 - Tectonic plate theory (From USGS [2])

Energy builds up in the earth’s crust as the tectonic plates converge, diverge, or transform, and

when the stresses of plate movement exceed the strength of the rocks of the earth, earthquakes

occur. These areas of plate collision are referred to as faults.


Thomas Ødegaard 16

2.2 Faults

There are three main types of faults; normal-, reverse-, and strike-slip fault. Normal faults occur

in areas where the tectonic plates are moving apart, reverse faults occur when the tectonic plates

converge, and strike-slip faults occur when the tectonic plates shear.

Figure 2-1 - Fault mechanisms (From Basic Earthquake Engineering [1])

Earthquakes are triggered by sudden raptures of these faults and are affected by combination fault

mechanisms. For practical reasons, the earthquakes are classified by the main contributing fault

mechanism. As the characteristics of the earthquake depend on the contributing fault mechanism,

this is considered in the selection of ground motions for use in time-history analysis.

2.2.1 Seismic waves

When faults rupture, seismic waves are discharged. These seismic waves have been classified into

four types:

Table 2-1 - Characteristics of seismic waves

Gro

un

d w

aves

Pressure waves (P-waves)

Approximately moving √𝟑 times than surface waves.

Arrives first, but usually yield a comparatively small contribution

to the overall ground motion.

Moves with compression and dilatations.

Can travel through solids, water and gass.

Shear waves (S-waves)

Moderate speed, arrives secondly. Moves with a shearing body

motion.

Comparative contribution to overall ground motion depends on

focal distance.

Can only travel through solids

Su

rface

waves

Surface waves:

Surface waves move the slowest and arrives last.

Travels long distances, making the comparative contribution to

ground motions large for sites with long focal distance.

Rayleigh wave

Movement similar to water-waves, which induces vertical effect on

structures.

Love waves

Movement in the horizontal directions, which contributes largely

to the horizontal effect on structures.

Figure 2-2 - Seismic waves (From Basic Earthquake Engineering [1])


Thomas Ødegaard 17

The properties defined for the different wave classifications are exemplified in the following

figure:

Figure 2-3 - Seismic waves - speed and magnitude correlation (From USGS [3])

2.3 Classification of earthquakes

With the focus of this thesis being on seismic design after Indian and European seismic design

codes, the classification relevant for these codes are discussed in this chapter.

The Eurocode is based on the moment- and surface wave magnitude scale, while the Indian

standard is based on the MSK-64 scale.

2.3.1 Moment- and surface wave magnitude

The moment- and surface wave magnitude scales are modifications to the Richter’s magnitude

scale. All are calculated from the energy dissipated during an earthquake, with measurements from

seismographs.

Moment magnitude, denoted Mw, is calculated from the seismic moment Mo. The seismic moment

is further a function of fault rapture area and average slip between the moving blocks. Moment

magnitude is then defined:

𝑀𝑊 =2

3𝑙𝑜𝑔10(𝑀0) − 6 (2.1)

There have been developed many formulations for calculating the surface wave-magnitude. A

commonly used formulation by Vanêk (1962 [4]) depend on amplitude of the surface waves (A),

the dominant period of vibration (T) and the distance from epicenter (∆).

𝑀𝑠 = 𝑙𝑜𝑔10 (𝐴

𝑇)𝑚𝑎𝑥

+ 1.66 𝑙𝑜𝑔10 ∆ + 3.33 (2.2)


Thomas Ødegaard 18

2.3.2 MSK-64

The MSK-64 (Medvedev-Sponheuer-Karnik) scale is an intensity scale defined by the observed

effects near the epicenter of an earthquake. It is very similar to the MMI (Modified Mercalli

Intensit) scale.

Table 2-2 - Comparison of MSK-64 and MMI classification

MSK-64 [5] MMI [6]

I Not noticable Not fealt

II Scarcely noticable Weak

III Weak, partially observed Weak

IV Largly observed Light

V Awakeniing Moderate

VI Frighenin|g Strong

VII Damage of buildings Very strong

VIII Destruction of buildings Severe

IX General damage of buildings Violent

X General destruction of buildings Extreme

XI Destruction Extreme

XII Landscape changes Extreme

As the MSK-64- and moment magnitude scales are based on different earthquake characteristics,

no accurate comparison can be made between the two. With this mentioned, USGS has made a

typical observed correlation of intensities and magnitudes:

Tabell 1 - Magnitude & Intensity comparison (From USGS [6])

Magnitude (Richter) Intensity (MMI)

1.0 – 3.0 I

3.0 – 3.9 II – III

4.0 – 4.9 IV – V

5.0 – 5.9 VI – VII

6.0 – 6.9 VII – IX

7 and higher VIII or higher


Thomas Ødegaard 19

2.4 Seismic Hazard Assessment

To determine the seismic hazard of any area, site or region, seismic hazard analysis is conducted.

These are mainly divided into two categories; deterministic (DSHA) and probabilistic (PSHA).

2.4.1 Probabilistic (PSHA)

In a PSHA, all earthquake scenarios that can be generated from a seismic source is considered for

the site in question. The seismic sources (faults) are characterized after the maximum moment

magnitude. Seismic hazard is then normally calculated with respect to PGA with a defined

probability of exceedance, e.g. PGA with 10% probability of exceedance in 50 years (475year

return period).

Figure 2-4 - Typical results of a PSHA (From Basic Earthquake Engineering [1])

2.4.2 Deterministic (DSHA)

In a DSHA, the seismic hazard is defined on the least favorable earthquake scenario for the project

site. All earthquake scenarios, with characteristics as source-to-site distance and magnitude, should

be evaluated. This approach will yield a more conservative representation for seismic hazard as it

does not reflect likelihood of seismic activity, only the possibility.


Thomas Ødegaard 20

2.5 Seismicity in Nepal

Nepal lies right on the collision boundary of the Indian- and Eurasian plate, in the Himalaya region.

The Himalaya region is geologically divided into the Higher Himalaya, sub-Himalaya, lesser

Himalaya, and Tethyan Himalaya. On the border of these geological divides you find the following

geological structures; the Main Frontal Thrust (MFT), Main Boundary Thrust (MBT), Main

Central Thrust (MCT), and South Tibet Detachment (STD). These are presented in Figure 2 -

Geological map of Nepal (From

Figure 2 - Geological map of Nepal (From Seismic risk assessment and hazard mapping in Nepal [7])

Earthquakes form in these thrust systems, and among these the most active faults lie in the MBT

and MCT. As the tectonic plates are converging, the most typical faulting mechanism of

earthquakes is reverse faulting.

The region is very seismic, with a number of significant earthquakes in the last century. A list

compiled of earthquakes with a magnitude of over 6.5 within the last century is presented in Table

2-3, with data from National Center of Environmental Information (NCEI) [8].

Table 2-3 - Earthquakes (>6.5Mw) in Nepal in the last century (From NCEI [8])

Year Month Magnitude Intensity

(MMI) Fatalities

1916 August 7.7Mw No data No data

1934 January 8.0Mw XI 10 600

1980 July 6.5Mw No data 200

1988 August 6.6Mw VIII 1 091

2015 April 7.8Mw VIII 8 857

2015 May 7.8Mw VII 117


Thomas Ødegaard 21

Further, the seismic hazard for Kathmandu for use in the case study is based on the conference

paper Comparative study of seismic hazard of Kathmandu valley, Nepal with other seismic prone

cities [9]. The paper suggests the following PGA-values based on PSHA:

Table 2-4 - PGA with probabilities of exceedance for Kathmandu, Nepal [9]

Probability of exceedance in 50 years PGA [g]

(PV) 50% 0.26

(DCE) 10% 0.49

(MCE 2% 0.76

The results presented in the study show a prominent correlation to other seismic prone cities, such

as Los Angeles, USA and Sendai, Japan.

Figure 2-5 - Comparison of PGA for Kathmandu city (Sunuwar 2005 [9])


Thomas Ødegaard 22

3 STRUCTURAL MODELLING AND ANALYSIS

This chapter will describe and discuss the process of modelling and analyzing concrete structures

using computer software. For the case study of this thesis the structural analysis software SAP2000

was used so the theory is focused towards this software but will most likely be applicable for

similar software.

3.1 Structural analysis elements

To perform a structural analysis all the structural elements needs to be idealized using elements

based on mathematical models. These elements are based finite element formulation. Represented

here are the elements that are necessary to model concrete structures. The theory in this chapter is

obtained from the CSI Analysis Reference Manual [10].

3.1.1 Frame elements

The frame elements are based on 3D finite elements beam formulation.

[𝐹] =

[ 𝑋 0 0 0 0 0 −𝑋 0 0 0 0 0

𝑌1 0 0 0 𝑌2 0 −𝑌1 0 0 0 𝑌2

𝑍1 0 −𝑍2 0 0 0 −𝑍1 0 −𝑍2 0

𝑆 0 0 0 0 0 −𝑆 0 0𝑍3 0 0 0 𝑍2 0 𝑍4 0

𝑌3 0 −𝑌2 0 0 0 𝑌4

𝑋 0 0 0 0 0𝑌1 0 0 0 −𝑌2

𝑍1 0 𝑍2 0

𝑆 0 0𝑍3 0

𝑌3 ]

⋅

[ 𝑢1

𝑣1

𝑤1

𝜃𝑥,1

𝜃𝑦,1

𝜃𝑧,1

𝑢2

𝑣2

𝑤2

𝜃𝑥,2

𝜃𝑦,2

𝜃𝑧,2]

(3.1)

This means that the element can describe displacements and rotations in x-, y-, and z-axis. Using

compatibility relations, bending-, axial- and torsional stresses and forces can be calculated. This

element is applicable to analyze three-dimensional columns and beams and are modeled as lines,

either straight or curved, between two points and can have properties that vary within its length.


Thomas Ødegaard 23

3.1.2 Shell elements

The shell elements are finite element area elements that can be used to model membrane, plate and

shell behaviors. In SAP2000 shell elements can either follow the four-node quadrilateral (Q4), or

the triangular finite element definition.

Figure 3-1 – Q4- and triangular shell elements in SAP2000 (From CSI Analysis Reference manual [10])

To gain accuracy in shell elements, meshing is applied to the shells. Again, the challenge is to find

the optimal balance between computational efficiency and accuracy of the results. This was

exemplified in the case study while modelling shear walls.

No meshing Max mesh size 800x800mm

Mode Period [s] Ux Uy Rz Period [s] Ux Uy Rz

1 0.32 4% 27% 22% 0.43 0% 46% 23%

2 0.27 14% 27% 0% 0.33 61% 0% 4%

3 0.23 31% 6% 24% 0.30 0% 22% 30%

4 0.20 14% 0 11% 0.22 7% 0% 10%

Figure 3-2 - Comparison of meshing options effect on modal analysis

Where Ux is displacement in x-direction, Uy is displacement in y-direction and Rz is torsional

rotation.

3.2 Diaphragm

The theory in chapter is obtained from the CSI Analysis Reference Manual [10].

The term diaphragm describes a structural element that transfers lateral loads to the vertical

structural-system and is thereby a very important modelling tool in seismic design of buildings. In

most structural systems the floors and roofs are designed to act as diaphragms, either rigid- or

semi-rigid, with provisions in the code on how to classify the diaphragm.

A rigid diaphragm assumes that in-plane stiffness of a structure is infinite. This assumption is

based on the notion that with sufficient in-plane stiffness, the in-plane deflection of floor is

neglectable. A typical rigid diaphragm consists of a concrete floor system with large in-plane

stiffness.


Thomas Ødegaard 24

With semi-rigid diaphragms the in-plane stiffness is smaller comparatively to the lateral force-

resisting system. The in-plane stiffness must then be calculated by the software, which makes it

more computational expensive. Examples of semi-rigid diaphragm are; light-weight floors of thin

concrete slabs, wood-frame floors, metal sheet roofing.

In SAP2000, diaphragm is assigned as joint constraints and can automatically be assigned for each

leap in elevation. It is important to only assign these constraints to joints that are connected by the

diaphragm component.

Figure 3-3 - Diaphragm behavior (From CSI Analysis Reference manual [10])

3.3 Nonlinear behavior

The nonlinear behavior of structural components is defined as the behavior of which the change

of input is not proportional to the change of the output. In structural analysis this behavior is mostly

considered as being related to material- or geometrical properties.

The theory in this subchapter is obtained from the CSI Analysis Reference Manual [10], Theory of

Nonlinear Structural Analysis: The Force Analogy Method for Earthquake Engineering [11] and

NIST – Guidelines for Nonlinear Structural Analysis for Design of Buildings [12] [13].


Thomas Ødegaard 25

3.3.1 Geometric nonlinearity

Geometric nonlinearity occurs when the displacement-strain relation behaves nonlinearly. This

results in changes to the stiffness matrix depending on the deflection of either the globally for the

whole structure (Large P-Delta – P-∆), or locally for each member (Small P-Delta – P-𝛿).

The two main computation methods for computing geometric nonlinearity are the P-Delta-, and

the geometric stiffness approach. The main difference of the two is that the P-Delta approach

neglects small P-Delta, the geometric approach includes it. This makes the P-Delta approach more

computational efficient for analysis of overall structural stability, while the geometric stiffness

approach is more precise and more suitable for design and verification of structural members. The

latter approach is implemented in SAP2000

For nonlinear analysis in SAP2000 three options when considering geometric nonlinearity;

• P-Delta plus large displacements:

Deformed shape is fully implemented in the equilibrium equations. The loading is

applied stepwise, and for each step the stiffness matrix is recalculated.

• P-Delta:

Deformed shape is partially implemented in the equilibrium equations.

The initial stiffness matrix is modified depending the initial deformation, making

the P-Delta procedure a one-step procedure.

• Not considered:

Undeformed configuration of structure and initial stiffness matrix is used in analysis

According to the reference manual, the P-Delta option is recommended for most cases of nonlinear

analysis, as the displacement range of geometric nonlinearity covered by this approach usually is

well within the limit of acceptable material nonlinearity.

3.3.2 Material nonlinearity

There are several ways to analyze the non-linear behavior of concrete frames in the state of the art

software. The balance between computational efficiency and precision is an important measure to

consider, and so there have been developed several idealizations analysis models depending on

where the balance is put.

Figure 3-4 - Section material nonlinearity models (From Guidelines for Nonlinear Structural Analysis for Design of Buildings [12])

In the case study of this thesis, there were used both concentrated plastic hinge and fiber hinges,

depending on the type of non-linear analysis performed. These are further discussed:


Thomas Ødegaard 26

3.3.2.1 Concentrated plastic hinge

When using concentrated plastic hinges, the nonlinear behavior is idealized to appear in zero-

length rotational springs. These hinges should be assigned to the points of the members most likely

to experience plastic deformation.

Figure 3-5 - Concentrated plastic hinges (From Guidelines for Nonlinear Structural Analysis for Design of Buildings [12])

The hinge-properties are most commonly defined as either M3 or P-M2-M3. M3-hinges are used

for elements for which plastic mechanism is mainly contributed by the bending moment along the

dominant axis, and so is typically used for beams in which axial force and sideways bending

moment can be neglected. P-M2-M3 are used for elements for which the plastic mechanism is

contributed by the interaction of axial force, and bending moment about both longitudinal axis,

and so is typically used columns.

Figure 3-6 - Moment-curvature (y-,x-axis) relation for plastic hinges in SAP2000. L.S M3-hinge, R.S P-M2-M3 Hinge

As the moment-curvature relation is well defined, the hinge states can easily be obtained. And, if

acceptance criteria for hinge rotation is defined, structural performance assessment on the basis of

hinge rotation can be efficiently performed.

In SAP2000 such hinge properties can be automatically defined on the basis of ASCE 41-13. These

hinges are created with an isotropic hysteresis model, which is found applicable for pushover

analysis. For nonlinear time history analysis, this hysteresis model is not recommended to use, and

either user-defined hinges or fiber hinges should be used in these instances.


Thomas Ødegaard 27

3.3.2.2 Fiber hinges

Fiber hinge idealization reduces the section into a number of fibers, each with its own nonlinear

parameters. Hinge properties can therefore automatically be defined on the basis of section

properties and material properties. This eliminates the uncertainties of selection of hysteresis

model for the hinge, making it a more suitable selection for use in time history analysis.

Figure 3-7 - Fiber type hinges - Conectrated plastic hinges (From Guidelines for Nonlinear Structural Analysis for Design of Buildings [3])

Figure 3-8 - L.S Column section, R.S generated fiber hinge

Fiber hinges though, are more computational expensive, both in analysis and in obtaining results.

In SAP2000 acceptance criteria based on hinge rotation cannot be assigned directly to the elements

and must evaluated in the post-processing of the results. Fiber hinges provides the option of

evaluating the stress and strain of each defined fiber, providing the possibility of thoroughly

evaluating the state of both the concrete rebar separately. This method of evaluating the hinge is

more accurate, but proves significantly more time-consuming, making it not as suitable for more

complex analytical models.

3.3.2.3 Nonlinear layered shell elements

SAP2000 also allows for material-nonlinear modelling of shells, by the use of nonlinear layered

shell elements. The shell element is defined and built up by layers of selected material properties

and thickness. Further it can be selected which layers, and in which directions (longitudinal,

horizontal, and transversal) that should be considered as nonlinear. This option provides the choice

of accuracy versus computational efficiency.

These elements are useful for modelling shear walls. The CSI analysis reference manual

recommends the following two nonlinear configurations for modelling of shear walls:


Thomas Ødegaard 28

Table 3-1 - Nonlinear shear wall modelling

“Realistic” “Practical”

Type 𝝈𝒙 𝝈𝒚 𝝈𝒙𝒚 𝝈𝒙 𝝈𝒚 𝝈𝒙𝒚

Concrete Membrane NL NL NL L NL L

Rebar Top Vert. Membrane NL - NL NL - -

Rebar Top Hor. Membrane NL - NL NL - -

Rebar Bot. Vert. Membrane NL - NL - - -

Rebar Bot. Hor. Membrane NL - NL - - -

Concrete Plate - - - L L L

In the case study the shear walls were modelled after the realistic approach:

Table 3-2 - Shear wall model used in case study

Type Thickness 𝝈𝒙 𝝈𝒚 𝝈𝒙𝒚

Concrete Membrane 230mm NL NL NL

Rebar Top Vert. Membrane 0.753mm NL - NL

Rebar Top Hor. Membrane 0.753mm NL - NL

Rebar Bot. Vert. Membrane 0.753mm NL - NL

Rebar Bot. Hor. Membrane 0.753mm NL - NL

Figure 3-9 - Shear wall model used in case study

3.4 Damping

The damping effect in structural dynamics is defined as the process by which free vibration steadily

diminishes in amplitude (p.12, [14]). In the equation of motion, damping coefficient C is linked to

the velocity.

𝑀�̈�(𝑡) + 𝑪�̇� + 𝐾𝑢(𝑡) = 𝐹(𝑡) (3.2)

Where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, F(t) is the loading

functions, and 𝑢, �̇� and �̈� is displacement, velocity and acceleration.

For structural dynamic purposes, the dissipation of energy is usually idealized as equivalent

viscous damping.

To idealize the viscous damping acting in a structure, there are generally two options:

3.4.1 Modal damping

A modal damping ratio, which is defined as the fraction of critical damping 𝜁/𝜁𝑐𝑟𝑖𝑡, is assigned to

designated modes. Damping is therefore not implemented directly into the equation of motion but


Thomas Ødegaard 29

assigned to results of a modal analysis. This approach is mostly used or analysis methods which

rely on modal analysis, e.g. response spectrum and modal time history.

3.4.2 Rayleigh damping

Damping is calculated as a mass- and stiffness-proportional damping, and unlike the modal

damping approach a full damping matrix is calculated for the equation of motion. This enables a

more accurate description of damping, as coupling between modes can be considered. Mass- and

stiffness proportional damping is combined in Rayleigh damping, which is defined as

𝐶 = 𝑎0𝑀 + 𝑎1K (3.3)

Where C is the damping matrix, M is the mass matrix, and K is the stiffness matrix.

The coefficients 𝑎0 and 𝑎1 can be calculated on the basis of predefined modes and designated

damping ratios:

1

2[1/𝜔𝑖 𝜔𝑖

1/𝜔𝑗 𝜔𝑗] {

𝑎0

𝑎1} = {

𝜁𝑖

𝜁𝑗} (3.4)

Where 𝜔 is mode of vibration and 𝜁 is damping ratio.

Figure 3-10 - Rayleigh damping (from Chopra [14])


Thomas Ødegaard 30

3.5 Torsion

In dynamic earthquake loading, torsional force can be quite significant, and is often the source of

damage in the perimeter of the structure. In both Eurocode 8 and IS1893 the torsional rigidity is

classified on the basis of center of mass, center of rigidity, torsional radius, and radius of gyration.

This subchapter introduces procedures to obtain these values from a structural analysis model:

Center of mass:

[𝑥𝑚, 𝑦𝑚] =∑ ([𝑥𝑖 , 𝑦𝑖] ⋅ 𝑚𝑖)

𝑛𝑖=1

∑ (𝑚𝑖)𝑛𝑖=1

(3.5)

Center of rigidity

[𝑥𝑟 , 𝑦𝑟] =∑ ([𝑥𝑖, 𝑦𝑖] ⋅ 𝑘𝑖)

𝑛𝑖=1

∑ (𝑘𝑖)𝑛𝑖=1

(3.6)

Where x and y are node coordinates, m is node mass, and k is lateral stiffness for the node.

If using a spatial model in analysis software that doesn’t provide automatic definition of center of

rigidity, the following procedure can be used:

Apply three load cases with point loads at the center of mass [𝑥𝑚, 𝑦𝑚].

Case 1: 𝐹𝑥 = 1𝑘𝑁 Case 2: 𝐹𝑦 = 1𝑘𝑁

Case 3: 𝑀𝑧 = 1𝑘𝑁𝑚

From the analysis results the eccentricities to the center of rigidity is found by the following

expression:

𝑒0𝑥 = −𝑀𝑧,𝑐𝑎𝑠𝑒 2

𝑀𝑧,𝑐𝑎𝑠𝑒 3 (3.7)

𝑒𝑜𝑦 =𝑀𝑧,𝑐𝑎𝑠𝑒 1

𝑀𝑧,𝑐𝑎𝑠𝑒 3 (3.8)

The coordinates to the center of rigidity is then [𝑥𝑚 + 𝑒0𝑥, 𝑦𝑚 + 𝑒0𝑦].

From the same analysis result the torsional radius can be obtained. The torsional radius is defined

by:

[𝑟𝑥, 𝑟𝑦] = [√𝐾𝑀

𝐾𝐹𝑦, √

𝐾𝑀

𝐾𝐹𝑥] (3.9)

Where:

KFx =1

𝑈𝑥(𝑥𝑚, 𝑦𝑚)𝐶𝑎𝑠𝑒 1 (3.10)


Thomas Ødegaard 31

KFy =1

𝑈𝑦(𝑥𝑚, 𝑦𝑚)𝐶𝑎𝑠𝑒 2 (3.11)

𝐾𝑀 =1

𝑅𝑧(𝑥𝑚, 𝑦𝑚)𝐶𝑎𝑠𝑒 3 (3.12)

Where U and R is the deflection and rotation of the node at center of mass.

To classify the structure according to Eurocode 8, the radius of gyration (ls) of the floor mass in

plan must be determined. The radius of gyrations is determined by the expression:

𝑙𝑠 = √𝐼

𝑀 (3.13)

With a spatial analysis model, the radius of gyration can be determined by the assembled joint

masses by:

𝑙𝑠 = √∑ (𝑚𝑖 ⋅ √(𝑥𝑖 − 𝑥𝑚)2 + (𝑦𝑖 − 𝑦𝑚)2)𝑛

𝑖=1

∑ (𝑚𝑖)𝑛𝑖=1

(3.14)

3.6 Modal

The modes of vibration of a structure provides much information about its behavior during seismic

action. To obtain these modes, a modal analysis is performed. The number of vibration modes

depends on the number degrees of freedom of the structural system, so for a spatial model the

number of mode is quite substantial. When performing modal analysis for use in response spectrum

or modal time history analysis, its therefore interesting to find the necessary amount of modes to

gain sufficient accuracy.

The parameter used to evaluate the accuracy of the modal analysis is the modal mass participation

ratio. This value represents the ratio of modal mass that is active in a deflection or rotation for a

given mass. When considering the amount of modes needed, the accumulated modal mass

participation ratio in the relevant directions is evaluated. Both IS1893 and Eurocode 8 sets demand

for minimum modal mass participation ratio.

For finding the modes, there are several approaches. The two most prominent, and which are

available in SAP2000 is further discussed:

3.6.1 Eigenvectors

When performing a modal-eigenvector analysis, the modes of vibration are found for the

undamped free vibration, i.e. natural modes, of the structural system:

𝑀�̈�(𝑡) + 𝐾𝑢(𝑡) = 0 (3.15)

[𝐾 − Ω2𝑀]Φ = 0 (3.16)


Thomas Ødegaard 32

Where 𝛺 is the diagonal matrix of eigenvectors and Φ is the corresponding mode-shape.

3.6.2 Ritz-vectors

When preforming a modal-ritz-vector analysis, the modes of vibration are found by seeking the

modes the modes that are excited by a set loading scheme:

𝑀�̈�(𝑡) + 𝐾𝑢(𝑡) = 𝑅(𝑡) (3.17)

To find the modes of vibration, dependent on the Ritz-loading, an algorithm is applied, presented

Table 15.4.1 of Dynamics of Structures [14].

This approach to modal analysis is especially beneficial for response spectrum and time history

analysis, as it considers the spatial distribution of dynamic loading. Modes that is not affected by

the chosen loading scheme, with no modal mass participation in relevant directions, are not

captured by the modal analysis, resulting in fewer modes to reach a target mass participation.

The main drawback of using Ritz-vectors is that the modes of vibration are only approximates of

the real eigenvectors

For modal analysis for use in response spectrum analysis, the loading used may be acceleration

forces in x-, y-, and z-direction.

3.7 Response spectrum analysis

Theory for response spectrum analysis is obtained from Dynamics of Structures [14].

As the peak force and displacements occur in the modes of vibration of the structure, these points

will be of particular interest in dynamic analyses. With response spectrum analyses, the spectral

acceleration is assigned the modes of vibration, from a modal analysis, and further combines the

peak values to obtain the seismic design forces and displacements.

3.7.1 Modal combination

If the peak modal responses are combined by simply adding all the peak response, the results will

be very conservative. From both Eurocode 8 and IS1893 it is recommended to either use SRSS-

or CQC-modal combinations to obtain seismic design forces.

3.7.1.1 SRSS

SRSS – square root of sum of squares – uses the following combination to obtain design forces:

𝑟𝑜 = √∑ 𝑟𝑛𝑜2

𝑁

𝑛=1

(3.18)

Where 𝑟𝑜 is the total response and 𝑟𝑛𝑜 is the induvial peak modal response.

This approach is sufficient for cases where modes of vibration are separated, and not closely space.

For cases of closely spaced modes, the CQC-combination should be used.

3.7.1.2 CQC

CQC – complete quadratic combination – uses the following combination to obtain design forces:


Thomas Ødegaard 33

𝑟𝑜 = √∑ ∑ 𝜌𝑖𝑛 ⋅ 𝑟𝑖𝑜2 ⋅ 𝑟𝑖𝑜

2

𝑁

𝑛=1

𝑁

𝑖=1

(3.19)

Where 𝜌𝑖𝑛 is a correlation coefficient between 0 and 1.

This approach considers the effect of closely space modes of vibration, and is therefore often

considered the most accurate approach.

3.8 Nonlinear static analysis

As the name indicates, in these analyses nonlinear behavior is analyzed using static forces. With

regards to seismic analysis, there are two main procedures that uses nonlinear static analysis; P-

Delta- and pushover analysis.

3.8.1 P-Delta

For seismic analysis the vertical loads/weights, which are defined for as the seismic weigh, are

applied in a static analysis. The purpose of such analysis is to determine the reduced stiffness with

the seismic weight applied.

In SAP2000 other nonlinear analysis can be conducted to start from the end state of a P-Delta

analysis. With this approach, the reduced stiffness and the vertical force from the P-Delta analysis

is incorporated in to the analysis of choice.

3.8.2 Pushover analysis

A pushover analysis is performed by incrementally applying a lateral static load which is

controlled by the displacement of an assigned control node, commonly assigned at roof level. The

lateral load pattern depends on the procedure chosen for the analysis, e.g. modal- or gravity load

pattern.

Figure 3-11 - Pushover curve

In the case study, a gravity lateral load pattern was used. This way the lateral force is applied at

each node depending only on the seismic mass. This will usually replicate the main mode of

vibration for the two horizontal axis.


Thomas Ødegaard 34

With the pushover analysis performed, the displacement of the control node is plotted against the

base shear to create the pushover curve. From the pushover curve the behavior of the structure can

be interpreted, i.e. in what range does it behave linearly and when does the plastic mechanisms

begin. With a seismic demand set, there can also be determined target displacements for a given

seismic hazard.

3.9 Time History Analysis

The theory of this chapter is obtained from Selection and Scaling Time History Records for

Performance-Based Design [15] and Guidelines for Nonlinear Structural Analysis for Design of

Buildings [13].

In a time-history analysis, the earthquake loading is represented in the form of accelerograms.

When performed correctly, it is considered the most accurate approach to determine seismic forces.

The accelerograms used in the analysis can either be recordings of real earthquakes, artificially

created to be compatible with design response spectrums, or synthetic records obtained from

seismological models. As large databases of ground motions from real earthquakes are readily

available, e.g. PEER Ground motion database [16], it is the type further considered and used in the

case study.

To get a good representation of the seismic forces expected to be prevalent at the project site, there

should be defined some criteria for selection of ground motions based on geological and

seismological conditions. The following characteristics should be considered, according to Fahjan

[15]:

- Magnitude

- Faulting mechanism

- Distance to fault

- Rupture directivity

- Site conditions (e.g. shear velocity)

- Spectral content

As the point of obtaining several ground motions is to provide variation, it is further recommended

to only use on set of ground motion per earthquake.

With the ground motion obtained, they need to be scaled or spectral matched to match the seismic

hazard level of the project site. This can either be obtained through the response spectrum from

the relevant code, or though site-specific PSHA. A common approach is to scale spectral

acceleration of the suite of ground motions to the spectral acceleration seismic demand at the most

prominent mode(s) of vibration of the structure.

With a suite of ground motions selected and scaled, the can be performed. In SAP2000 there are

two categories of time-history analysis; modal and direct integration, both of which can be

analyzed either linearly or nonlinearly.

3.9.1 Modal time-history analysis

Modal time-history is by far the most computational efficient approach. It uses the same theoretical

background as the response spectrum analysis, while instead of calculating peak modal responses,

the modal response is calculated for each time step (Chapter 13.1 Chopra [14]).

In SAP2000 there is the possibility of nonlinear modal time-history analysis, referred to as Fast

Nonlinear Analysis (FNA). This approach is suitable for load cases which is primarily linearly, and


Thomas Ødegaard 35

only a small degree of nonlinearity is expected. The nonlinear behavior is lumped into link-

elements, which simplifies the nonlinear relation of the equation of motion to:

𝑀�̈�(𝑡) + 𝐶�̇�(𝑡) + 𝐾𝐿𝑢(𝑡) + 𝑟𝑁(𝑡) = 𝑟(𝑡) (3.20)

Where KL is the stiffness matrix for linear elastic elements, and rN is the vector forces from the

nonlinear behavior of the link-elements.

3.9.2 Direct integration time-history analysis

In direct integration procedures the linear equations of motion are fully integrated:

𝑀�̈�(𝑡) + 𝐶�̇�(𝑡) + 𝐾𝑢(𝑡) = 𝐹(𝑡) (3.21)

Direct integration methods are very computational expensive, as for each step. The results obtained

are very accurate.

To perform the direct integration several algorithms can be used, among these the Newmark and

Hilbert-Hughes-Taylor (HHT) algorithms is available in SAP2000. The main difference between

the two is that HHT allows for additional damping of high frequency modes. This comes in handy

when using unprocessed ground motion, as the noise in high frequencies can be damped out in the

analysis.


Thomas Ødegaard 36

4 ANALYSIS AND DESIGN GUIDELINES TO EVALUATE SEISMIC ACTION

This chapter provides an overview of regulations regard seismic design for Eurocode 8, IS1893,

and PBSD methodology following guidelines from FEMA and ASCE.

As earthquake force are so significant, and with long return periods, the probability of a large

earthquake to occur in the lifespan of a structure is low. It is therefore normal practice to allow for

some damages to the structure in these rare events. The degree of allowable damage depends

mostly on the importance of building, as a hospital should remain operational in larger earthquake.

4.1 Eurocode 8-1

This chapter contains the requirements and recommendations to perform seismic analysis

following Eurocode 8 [17]. In the cases that it can be chosen between values recommended by the

code, or values regulated by the national annex, the code recommendations are followed.

Eurocode 8 does, to a small degree, implement PBDS methodology in its criteria. For a seismic

design to comply with the code, it has to fulfill both its Damage limitation and No collapse

requirements. The degree of implementation of the damage limitation limit is dependent on the

national authorities, for instance in Norway this limit state is not considered.

4.1.1 Seismic Hazard

In the Eurocode, the seismic hazard is defined on the basis of peak ground acceleration, the ground

type, and the surface wave magnitude of the earthquakes considered in a probabilistic seismic

hazard analysis.

The seismic hazard considered for the limit states of Eurocode is set by the national authorities,

while the recommended seismic hazard is:

Damage limitation 10% in 10 years 95year return

No collapse 10% in 50 years 475year return

To account for the difference in importance of buildings, an importance factor is implemented in

the peak ground acceleration. This way, the PGA with return period considered to fulfill the

damage limitation requirements are higher for hospitals than for houses. The following

approximation can be done according to clause 2.1(4) for an area of high seismicity (k=4).

Table 4-1 - Design ground accelerations correlated to return period

PGA I=0.7 I=1 =1.2 I=1.4

Damage limitation 𝑎𝑔,95𝑦𝑒𝑎𝑟 ~𝑎𝑔,50𝑦𝑒𝑎𝑟 𝑎𝑔,95𝑦𝑒𝑎𝑟 ~𝑎𝑔,225𝑦𝑒𝑎𝑟 ~𝑎𝑔,365𝑦𝑒𝑎𝑟

No collapse 𝑎𝑔,475𝑦𝑒𝑎𝑟 ~𝑎𝑔,50𝑦𝑒𝑎𝑟 𝑎𝑔,475𝑦𝑒𝑎𝑟 ~𝑎𝑔,50𝑦𝑒𝑎𝑟 ~𝑎𝑔,2000𝑦𝑒𝑎𝑟


Thomas Ødegaard 37

An elastic horizontal design spectrum is then established on the basis of design peak ground

motion, ground type and seismicity of the region.

Figure 4-1 - Type 1 & 2 horizontal response spectrum, behavior factor not included (From EC8 [17])

The Type 1 response spectrum is used in regions of high seismicity(>5.5Ms), while Type 2 is used

in regions with low seismicity (<5.5Ms).

4.1.2 Classifications

Many of the parameters of analysis is dependent on classifications regarding structural system,

regularity and ground types. These classifications are further discussed in the following sub-

chapters:

4.1.2.1 Structural system

The structural system is classified after the Eurocode as follows:

Frame system Structural system where 65% of total base shear sustained

by a beam- column system

Dual system Vertical loads mainly supported by columns, lateral loads

supported by both columns and structural walls

Wall-equivalent

When the structural walls obtain more than 50% of total

shear resistance.

Frame-equivalent

When the frame system obtains more than 50% of total

shear resistance

Wall system Where structural walls resist both lateral- and vertical

loads. Walls resist more than 65% of lateral force

Coupled/

Uncoupled

Structural walls are coupled if two more walls are

connected by ductile beams, in a regular pattern.

Torsional flexible system Dual- and wall system which does not provide the

minimum torsional rigidity required by the code.

Inverted pendulum system Structural systems where the upper third of the structure

contains over 50% of the total mass


Thomas Ødegaard 38

Some of these structural classifications comes with further regulations/benefits. For concrete wall-

equivalent dual frame the interaction of masonry infills, which for instance is a component much

used in concrete frame structures in Nepal.

To determine if the structure is torsional flexible, it needs to satisfy the following condition, where

the eccentricity, radius of gyration, and torsional radius is defined in Chapter 3.5.

[𝑟𝑥, 𝑟𝑦] ≥ 𝑙𝑠 (4.1)

[𝑒0𝑥, 𝑒0𝑦] ≤ [0.3𝑟𝑥, 0.3𝑟𝑦] (4.2)

4.1.2.2 Regularity

The Eurocode classify structural systems as either regular- or irregular in plan and elevation. The

criteria to evaluate structural regularity is well defined in chapter 4.2.3.

The Eurocode rewards buildings with regularity in plan and elevation with greater reduction

regarding the buildings ductility, and with simpler forms of dynamic analysis. This is due to the

limitation of torsional forces in regular designs, and the mode shape which regularity provides.

For non-linear static analysis, plan regular buildings are also allowed the simplification of planar

analysis, while plan irregular buildings must be analyzed by a spatial model.

4.1.2.3 Ground types

The effect of site soil conditions is accounted for by the ground types. These are characterized by

soil classification, shear wave velocity, SPT value, and the undrained shear strength of the soil. As

the geotechnical report provided for the case study only contains SPT values, this is presented in

Table 4-2 and further compared to the classes of IS1893. Full list of ground types is found in Table

3.1 in Eurocode 8-1.

Table 4-2 – equivalent SPT values for soil types

SPT-value

Type A Rocks -

Type B Very dense sand, gravel, or very stiff clay >50

Type C Dense sand, gravel, or stiff clay 15-50

Type D Loose-to-medium cohesionless soil <15

Per clause 4.3.1(9), soil structure interaction may always be considered even if it will have a

beneficial effect, while for situations where SSI it thought to have adverse effect it is required to

be included in the analysis model.

4.1.3 Analysis model

On a global level, the Eurocode has a set of requirements for the type analysis model allowed. The

analysis model can either be planar or spatial, with the requirement being regularity in plan which

is further discussed in chapter.


Thomas Ødegaard 39

Table 4-3 - Analysis models depending on structural regularity

Regularity Allowed Simplification Behavior factor

Plan Elevation Model Linear-elastic Analysis (for linear analysis)

Yes Yes Planar Lateral Force Referenced value

Yes No Planar Modal Decreased value

No Yes Spatial Lateral Force Referenced value

No No Spatial Modal Decreased value

For linear elastic analysis, the flexural and shear stiffness properties should be modified to

represent the cracked moment of inertia. The recommended reduction in moment- and shear

stiffness is 50% of the corresponding stiffness of the uncracked elements. Reduction of torsional

constant to account for cracked torsional stiffness is not included in the code but is a recommended

practice in Seismic Design of Concrete Buildings to Eurocode 8 [18]. The torsional constant is

recommended set at 10% of uncracked torsional stiffness. This applies to all beam-, column- and

slab sections.

To transfer lateral loads to the vertical structural system, diaphragms should be assigned.

Diaphragms may be either rigid, or semi-rigid depending on the ratio between the in-plane stiffness

of the diaphragm and the lateral stiffness of the vertical system. The limit of when a diaphragm

should be considered semi-rigid or assumed rigid is not defined. For concrete structures, floor slabs

of over 70mm can be considered to serve as diaphragms.

When considering the base constraints of the structural model, the foundation of the building and

soil properties of the site must be considered. If foundation deformability is thought to have an

adverse effect on the building, soil-structure interaction should be included in the model. When

this is not the case it is allowed to model with more simplified constraints, for example pinned or

fixed.

4.1.4 Behavior Factor

In the Eurocode there are three ductility classes for structural analysis; DCL, DCM, and DCH (DC

– Ductility Class). The ductility class of the structure is based on its ability to sustain post-yield

loading, i.e strength in the non-linear domain.

For the different ductility classes there are different values for a behavior factor. This behavior

factor is used to reduce earthquake force in the linear elastic analysis and sets a limit for what

portion of the seismic loading is to be sustain within the linear-elastic domain of the structure. This

allows for some permanent deformation and damage to the structure in the event of rare

earthquakes.

The behavior factor also considers factors such as:

• Structural classification

• Regularity in plan and elevation

• Multiplication factor (𝛼𝑢/𝛼1) based on:

o Approximate values from the code depending on structure type, and number of

bays and stories.


Thomas Ødegaard 40

o Overstrength ratio obtained through a nonlinear static procedure (Pushover

analysis)

Further details on the use of pushover analysis is discussed in chapter 3.8.2.

Table 4-4 - Initial behavior factor

STRUCTURAL TYPE 𝒒𝟎 DCM 𝒒𝟎 DCH

Frame system, dual system, coupled wall system 3,0 𝛼𝑢/𝛼1 4,5 𝛼𝑢/𝛼1

Uncoupled wall system 3,0 4,0 𝛼𝑢/𝛼1

Torsionally flexible system 2,0 3,0

Invereted pendulum system 1,5 2,0

The behavior factor is further defined as:

𝑞 = 𝑞0 ⋅ 𝑘𝑤 ⋅≥ 1.5 (4.3)

Where the factor kw depends on the structural system classification.


Thomas Ødegaard 41

4.1.5 Linear elastic analysis

For all linear elastic analysis, a design horizontal response spectrum is established on the basis of

the elastic horizontal response spectrum and the behavior factor q.

Figure 4-2 - Design horizontal response spectrum

For both methods of analysis, it should be evaluated if P-∆ effect should be considered by the use

of inter-story drift sensitivity coefficient:

4.1.5.1 Lateral force method

The simplest seismic analysis form is the lateral force method. For it to be applicable the following

criteria must be met:

• The fundamental period of vibration in the two main directions must fulfill:

𝑇1 ≤ {4 ⋅ 𝑇𝑐

2.0𝑠} (4.4)

• The structure must be regular in elevation

If these criteria are met, the base shear for each horizontal direction can be determined by:

𝐹𝑏 = 𝑆𝑑(𝑇1) ⋅ 𝑚 ⋅ 𝜆 (4.5)

Where 𝑆𝑑(𝑇) is the horizontal design spectrum, m is the total mass of the building above the

foundation level and 𝜆 is a correction value which considers the effective modal mass of the

building depending on its height.

The fundamental period of the structure can either be obtained through a modal analysis, or

through simplified approximations provided by the code. These approximations take into

consideration the material of the structural system and the height of the building.

Further, the lateral force is distributed to the floors either linearly if the fundamental period is

approximated, or dependent on the mode shapes if modal analysis is used:


Thomas Ødegaard 42

𝐹𝑖 = 𝐹𝑏 ⋅𝑧𝑖𝑚𝑖

∑𝑧𝑗𝑚𝑗 (4.6)

𝐹𝑖 = 𝐹𝑏 ⋅𝑠𝑖𝑚𝑖

∑𝑠𝑚𝑗 (4.7)

Where z is height from the base of the building, m is the mass of the story, and s is the displacement

off masses in the fundamental mode shape.

4.1.5.2 Modal response spectrum analysis

To conduct a modal response spectrum analysis, a set of requirements are set to the modal analysis:

• The sum of effective modal masses considered must be at least 90%

• All modes with modal mass greater than 5% must be considered

These requirements must be met for all directions considered for the response spectrum analysis.

Special conditions apply for structures with significant effects from torsional modes.

The combination of modal response can be obtained either by SRSS or CQC, established in chapter

3.7.1.

4.1.6 Nonlinear Static Analysis (Pushover)

According to EC8, pushover analysis can be used for the following purposes:

• to verify or revise the overstrength ratio values 𝛼𝑢/𝛼1

• to estimate the expected plastic mechanisms and the distribution of damage

• to assess the structural performance of existing or retrofitted buildings for the purposes of

EN 1998-3

• as an alternative to design based on linear-elastic analysis which uses the behavior factor

q. In that case, the target displacement indicated in 4.3.3.4.2.6 (1) should be used as the

basis of the design.

The lateral load pattern used depends on the procedure used. Assumptions and limitations of the

selected procedure should be carefully regarded. In the N2-method proposed by the Eurocode,

there is to be made to load cases, one for each direction. The later loading scheme can be defined

by a uniform – incrementally increasing – lateral gravity loading. This is further discussed in

chapter 3.8.2.

4.1.6.1 N2-method for target displacement

The procedure for determining a target displacement for a pushover analysis is presented in Annex

B of EC8. This procedure is otherwise referred to as the N2-procedure (nonlinear analysis in two

directions). The basic principle is to transform the structural model (MDOF) in to SDOF so that

the elastic response spectrum can be used, develop an idealized elasto–perfect plastic force-

displacement relationship from the pushover curve, and use this information to determine a target

displacement where analysis results should be collected from.

The following relation between story mass mi, normalized lateral force 𝐹�̅�, and normalized

displacement Φ𝑖:

𝐹�̅� = 𝑚𝑖Φ𝑖 (4.8)


Thomas Ødegaard 43

The displacement pattern is then normalized so that the roof displacement is Φ𝑛 = 1. This relation

can either be decided by the engineer or obtained from actual deformation of the pushover analysis.

The mass of equivalent SDOF system is defined as:

𝑚∗ = ∑𝑚𝑖Φ𝑖 = ∑𝐹�̅� (4.9)

MDOF structural model results can then transformed to a SDOF by a transformation factor:

Γ =𝑚∗

∑(𝑚𝑖Φ𝑖2)

=∑(𝑚𝑖Φ𝑖

2)

∑(𝑚𝑖Φ𝑖2)

=∑𝐹�̅�

∑(𝐹�̅�

2

𝑚𝑖)

(4.10)

𝐹∗ =𝐹𝑏

Γ (4.11)

𝑑∗ =𝑑𝑛

Γ (4.12)

With the pushover curve transformed to a SDOF system, the idealized elasto-perfect plastic force-

displacement can be determined. The N2-procedure uses bi-linearization to approximate the

pushover curve, assuming no stiffness after reaching plastic mechanism (A). The bi-linearization

is made so that the area above- is equal to the area below the transformed pushover curve, shown

in grey in Figure 4-3 - Bilinearization of the idealized pushover curve (From Annex B of EC8)

Figure 4-3 - Bilinearization of the idealized pushover curve (From Annex B of EC8 [17])

First, the displacement of which the plastic deformation occurs must be obtained. This point

introduces some uncertainty, as most pushover curves will not be as regular as the one in Figure

4-3 - Bilinearization of the idealized pushover curve (From Annex B of EC8).

With the displacement at plastic formation (dm*), the yield displacement can be found by the

following relation:

𝑑𝑦∗ = 2(𝑑𝑚

∗ −𝐸𝑚

∗

𝐹𝑦∗) (4.13)


Thomas Ødegaard 44

Where 𝐸𝑚∗ is the deformation energy up to displacement dm

*. This is defined as:

𝐸𝑚∗ = ∫ 𝐹∗(𝑑∗) 𝑑𝑑∗

𝑑𝑚∗

0

(4.14)

From software such as SAP2000 the output of pushover analysis is in the form of incremental data

points, and not a pure function. The deformation energy can then be found by the trapezoidal

method:

𝐸𝑚∗ = ∑ (

(𝐹𝑖−1 + 𝐹𝑖)

2⋅ (𝑑𝑖 − 𝑑𝑖−1))

𝑑𝑚∗

𝑖=𝑑1

(4.15)

With the yield displacement and base shear determined, the period of the idealized system is

determined:

𝑇∗ = 2𝜋√𝑚∗𝑑𝑦

∗

𝐹 (4.16)

The target displacement for a system assumed to behave purely elastic is given by:

𝑑𝑒𝑡∗ = 𝑆𝑒(𝑇∗) [

𝑇∗

2𝜋]2

(4.17)

Where 𝑆𝑒(𝑇∗) is the elastic response spectra defined in chapter 4.1.1.

Further determination of the target displacement depends on which range – short- or medium-long

range – the structural period lies. If in the short range (𝑇∗ < 𝑇𝑐):

First it’s determined if the structural response is elastic or in-elastic by the relation:

𝐹𝑦∗

𝑚∗≥ 𝑆𝑒(𝑇∗) (4.18)

If the relation is true the structural response is elastic, and the target displacement is equal to eq.

(4.17)

𝑑𝑡∗ = 𝑑𝑒𝑡

∗ (4.19)

If the relation is false the structural response is inelastic, and a factor qu is introduced which

represents the ratio between the system of limited strength and the elastic response spectra:

𝑞𝑢 =𝑆𝑒(𝑇∗) ⋅ 𝑚∗

𝐹𝑦∗

(4.20)

The target displacement is then defined as:


Thomas Ødegaard 45

𝑑𝑡∗ =

𝑑𝑒𝑡∗

𝑞𝑢(1 + (𝑞𝑢 − 1)

𝑇𝑐

𝑇∗) 𝑤ℎ𝑖𝑙𝑒 [

𝑑𝑡∗ ≥ 𝑑𝑒𝑡

∗

𝑑𝑡∗ ≤ 3𝑑𝑒𝑡

∗ ] (4.21)

If the structural period is in medium-long range (𝑇∗ ≥ 𝑇𝑐), the target displacement is defined as:

𝑑𝑡∗ = 𝑑𝑒𝑡

∗ (4.22)

When the proper target displacement is defined it is then transformed back to the MDOF system:

𝑑𝑡 = 𝑑𝑡∗ ⋅ Γ (4.23)

At the target displacement the result parameters can then be evaluated to see if the structure fulfills

the rest of the code, and if performance of the system is acceptable.

4.1.6.2 Overstrength factor

From the pushover analysis you can also obtain a correction to the behavior factor through the

overstrength factor. This is described in clause 5.2.2.2 (4) for concrete structures. The overstrength

factor consist of the factors 𝛼𝑢 and 𝛼1, which are defined as:

𝛼1

“.. the value by which the horizontal seismic design is multiplied in order to first

reach the flexural resistance in any member in the structure, while all other design

actions remains constant”

𝛼𝑢

“.. the value by which the horizontal seismic design action is multiplied in order to

form plastic hinges in a number of sections sufficient for the development of overall

structural instability, while all other design actions remain constant”

Both these factors can be obtained by the pushover analysis. 𝛼𝑢 can be determined graphically in

the same manner as the plastic mechanism defined in chapter 4.1.6.1. There are several ways to

determine 𝛼1, a very convenient way in SAP2000 is to determine this through hinge rotation. If

fiber hinges are used, a yield rotation must be defined. If lumped plasticity hinges following FEMA

356, the yield rotation can be found automatically and is graphically displayed in the results,

making for a much easier procedure.

A preliminary response spectrum analysis must also be completed beforehand, with the original

behavior factor. This is done to ensure that the linear elastic analysis is in the elastic region.


Thomas Ødegaard 46

Figure 4-4 - Pushover analysis - overstrength factor

With the base shear from the preliminary response spectrum analysis and the first local- and fully

plastic- yield base shear points, the factors can then be calculated:

𝛼1 =𝐹𝐹𝑖𝑟𝑠𝑡 𝑙𝑜𝑐𝑎𝑙 𝑦𝑖𝑒𝑙𝑑

𝐹𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒 𝑠𝑝𝑒𝑐𝑡𝑟𝑢𝑚 (4.24)

𝛼𝑢 =𝐹𝐹𝑢𝑙𝑙𝑦 𝑝𝑙𝑎𝑠𝑡𝑖𝑐 𝑦𝑖𝑒𝑙𝑑

𝐹𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒 𝑠𝑝𝑒𝑐𝑡𝑟𝑢𝑚 (4.25)

𝜶𝒖

𝜶𝟏=

𝑭𝑭𝒊𝒓𝒔𝒕 𝒍𝒐𝒄𝒂𝒍 𝒚𝒊𝒆𝒍𝒅

𝑭𝑭𝒖𝒍𝒍𝒚 𝒑𝒍𝒂𝒔𝒕𝒊𝒄 𝒚𝒊𝒆𝒍𝒅 (4.26)

This value can further be used to correct the behavior factor in Table 4-4 - Initial behavior factor.

4.1.7 Time History Analysis

Selection of ground motion should consider the following criteria:

• Fault distance

• Magnitude

• Site ground type

After selecting applicable ground-motions you have the option of either scaling, or spectral-

matching, the ground motions to the design response spectrum for the given case. There are here

two requirements for the selected records:

• At zero-period, the mean spectral acceleration for all the records must be greater than the

value of 𝑆 (soil amplification factor) ⋅ 𝑎𝑔.

• Between 0.2T1 and 2T1, where T1 is the fundamental period in the direction considered,

the mean spectral acceleration should not be less than 90% of the design spectrum.


Thomas Ødegaard 47

There is the option to either use three- or seven ground motion records for the analysis. If three

records are used, the design parameters are taken from the least favorable results. If seven records

are use the design parameters is derived from the average of the results.

For linear time history analysis, the ground motions are scaled according to the design horizontal

response spectrum, while for nonlinear time history analysis the ground motions are scaled

according to the elastic response spectrum.

The results from a linear time history analysis can be used to:

• Determine design forces for section design

• Determine inter-story drift for damage limitation demand

The results from a nonlinear time history analysis can be used to:

• Determine true inter-story drifts

• Determine plastic hinge rotation, and subsequently limit states according to EC8-3

4.1.8 Damage limitation – Drift limits

Due to the low seismicity in Norway, the damage limitation limit state is not required. As the case

study is located in an area of high seismicity, the requirements of damage limitation are therefore

relevant.

Per the Eurocode, structures should endure moderate earthquakes with little or no damage. For the

overall structural this requirement is met by satisfying the drift limits in clause 4.4.3.2

Table 4-5 - Drift limits - Damage limitation

𝒅𝑰

𝑯𝒊≤

𝟎. 𝟎𝟎𝟓

𝝂 Structures with brittle non-structural elements

𝒅𝑰

𝑯𝒊≤

𝟎. 𝟎𝟎𝟕𝟓

𝝂 Structures with ductile non-structural elements

𝒅𝑰

𝑯𝒊≤

𝟎. 𝟎𝟏

𝝂 Structures with non-interfering non-structural elements

Where Hi is the story height, 𝜈 is a reduction factor to find the equivalent drift for different return

periods. The inter-story drifts dI is calculated as:

𝑑𝐼 = 𝑞𝑑(𝑑𝑒,𝑖 − 𝑑𝑒,𝑖−1)

Where qd usually is chosen to be the same as behavior factor q, de denotes displacement obtained

from linear elastic analysis, and i denotes story.

Further requirements are recommended for buildings of civil importance, per clause 4.4.3.1 (2):

“Additional damage limitation verifications might be required in the case of buildings important

for civil protection or containing sensitive equipment.”. These additional verifications should be

incorporated in the national annex of the Eurocode. As there are no requirements provided by the

Norwegian national annex, further requirements might be obtained from other codes. For instance,

the damage limitation demand coincides with the Operational-performance level from ASCE 41-

13 presented in chapter 4.4.2.


Thomas Ødegaard 48

4.2 IS1893

In the Nepali Building Code (NBC 105) it is stated that it should be applied in conjunction with

the Indian code of seismic design. With only minor differences, it is therefore more practical to

use the Indian Code as it is substantially more detailed and is implemented in many commercial

software.

4.2.1 Seismic hazard

The peak ground acceleration is determined by the following zone-map in figure #. Per NCB Nepal

should be considered as zone 5 after the Indian standard. This map was made on the basis of

deterministic seismic hazard analysis.

Figure 4-5 - Seismic zone map of India (from IS1893 [5])

Table 4-6 - Zone factors for IS1893

MSK Intensity

Zone factor

(PGA [g])

Zone 2 VI or less 0,10

Zone 3 VII 0,16

Zone 4 VIII 0,24

Zone 5 IX and above 0,36

The PGA is based on the MSK intensity scale and approximates earthquake with 475year return

period. In the previous version of IS1893 (2002), it was differentiated between the design

earthquake (DE – approximately 95-year return) and maximum considered earthquake (MCE –

approximately 95-year return). This differentiation is left out in the new version of IS1893 (2016),

and it is only operated with a design seismic action of Z/2, which approximates a return period of

95-years.

Per clause 6.3.3.1 the vertical effect of earthquakes should be considered if; the building is in

seismic zone 4 or 5, the building is irregular in plan or elevation, or the building is rested in soft

soils.


Thomas Ødegaard 49

4.2.2 Classifications

There is assigned a number of classifications to the structure and site to determine the seismic

demand and response of the structure after IS1893

4.2.2.1 Structural system

The structural system is mainly classified into three types; Frame-, wall-, and dual structural

systems. Based on the ductility of the chosen structural system, further sub-classifications are made

to determine a behavior factor for the structure.

There is made a clear distinction for frame systems between Ordinary Moment Resisting Frames

(OMRF) and Special Moment Resisting Frames (SMRF). To be able to classify the frame-

system as SMRF it is required that the structure must comply with IS 13920 – Ductile

detailing of reinforce concrete structures subjected to seismic forces [19]. Ductile shear

walls are also required to comply with this standard.

4.2.2.2 Ground Types

In IS1893 soil types are classified into three types, presented in Table 2 in IS1893. When

examining the site using standard penetration testing, the classification of the soil material

combined with the following SPT-values are used to classify the soil type:

Table 4-7 – equivalent SPT values for soil types

SPT-value

Type A – Rock or hard soils >30

Type B – Medium or stiff soils 10-30

Type C – Soft soils <10

The choice of structural system is limited by the seismic zone.

4.2.2.3 Regularity

The criteria for regularity in plan and elevation is well defined in table 5 and 6 in IS1893. Two

criteria are though highlighted, as these differ significantly from Eurocode 8, and are especially

relevant for the case study:

Torsional irreguliarty:

Torsional irregularity is classified byc the difference in lateral deflection at of the two sides of the

building. Three limits are defined by Table 5 in IS1893. In opposition to Eurocode 8, IS1893 does

not allow for significanlty torsional irregular structural configruations:

∆𝒎𝒂𝒙

∆𝒎𝒊𝒏 ≤ 𝟏. 𝟓 Torsionally regluar

𝟐 ≥∆𝒎𝒂𝒙

∆𝒎𝒊𝒏 ≥ 𝟏. 𝟓

Complient if; the fundamental torsional mode shall be smaller than the

two horizontal, and three dimensional analysis is conducted

∆𝒎𝒂𝒙

∆𝒎𝒊𝒏 ≥ 𝟐. 𝟎 Not complient, building configuration should be revised.


Thomas Ødegaard 50

Figure 4-6 - Criteria for torsional regularity

Requirements for seismic zone IV and V:

For structures in seismic zone IV and V, additional criteria are defined. The first three modes of

vibration should account for an accumulative 65% modal mass participation in each principle plan

direction, and the fundamental periods should differ by at least 10%:

𝑇2 ≤ 0.9𝑇1


For linear-elastic analysis the moment of inertia shall be taken as 70% of gross moment of inertia

of columns, and 35% for beams.

Soil structure interaction can be included, but in simplification can be made by modelling as fixed

constraints if the soil is not thought to have a negative impact on the analysis results. In most cases,

the inclusion of soil structure interaction will yield conservative results as the soil will sustain a

portion of the dissipated energy in an earthquake.

Regarding the use of spatial or planar analysis model, clause 7.2.2 requires that the analysis model

should adequately represent irregularities in the structural configurations. The choice of analysis

model is therefore dependent on the interpretation of adequately.

4.2.4 Behavior factor

In IS1893 the allowance of nonlinear behavior at design level earthquake is based on the behavior

factor R, ranging from 1 (brittle) to 5 (highly ductile). In IS1893, this value is solely dependent on

the chosen structural system, further explained in chapter 4.2.2.1.


For the linear elastic analysis, a design horizontal acceleration spectrum is defined on the basis of

a horizontal seismic coefficient Ah:

𝐴ℎ =(𝑍2) (

𝑆𝑎

𝑔 )

(𝑅𝐼 )


Thomas Ødegaard 51

Where Z is zone factor, R is the behavior factor, I is the importance factor, and Sa /g is the spectral

acceleration dependent on the ground type. The linear elastic analysis can either be performed by

lateral force method or response spectrum analysis.

Figure 4-7 - Design horizontal response spectrum for response spectrum analysis - IS1893

Figure 4-8 - Design horizontal response spectrum for lateral force method - IS1893

4.2.5.1 Lateral force method

In the lateral force method, the total base shear is determined by:

𝑉𝐵 = 𝐴𝐻𝑊 (4.27)

Where AH is the horizontal seismic coefficient, and W is the seismic weight of the building. The

modes of vibration can either be found by a modal analysis, or be approximated in a similar manner

of Eurocode, according to clause 7.6.2 of IS1893. The total base shear is to be distributed linearly

by the same procedure as in Eurocode 8 (Equation (4.6, chapter 4.1.5.1).


Thomas Ødegaard 52

4.2.5.2 Modal response spectrum analysis

The following criteria is set for the modal response spectrum analysis:

• The sum of effective modal masses considered must be at least 90%

• Modes with periods of less than 0.03s can be cut off

• Modes may be combined by CQC

• The response spectrum should be scaled so that base shear is equivalent to that of the lateral

force method (Equation (4.27))

4.2.6 Drift limits

Per clause 7.11.1 of IS1893, the interstory drift should be less than 0.4%. The interstory drifts

should be obtained by the unscaled service level seismic loading.

𝑑𝐼 < 0.4% (4.28)

4.3 NBC 105

As noted in the previous chapter, the Nepali building code for seismic design (NBC105 [20]) is

very similar to IS1893. This chapter will highlight some of the differences between the two.


In a different approach than both Eurocode 8 and IS1893, NBC105 does not represent the ground

acceleration factor in relation to earthquake intensity directly. Instead, the ground acceleration of

Kathmandu is incorporated into the horizontal response spectrum, with the zone-factor functioning

as a reduction factor.

Figure 4-9 - Seismic zones (NBC 105 [20])

When comparing the seismic demand for Kathmandu, NBC105 and IS1893 (seismic zone V)

yields nearly identical seismic demands.


Thomas Ødegaard 53


The behavior factor K, described as structural performance factor by NBC105, is oriented in the

opposite order of IS1893 and Eurocode 8. A behavior factor of 1 represents the highest ductility

available, and a behavior factor of 5 represents a completely brittle behavior.


In NBC105 the design horizontal response spectrum is established on the basis of horizontal

seismic force coefficient Cd.

𝐶𝑑 = 𝐶 ⋅ 𝑍 ⋅ 𝐼 ⋅ 𝐾 (4.29)

Where C is a spectral acceleration function, Z is the zoning factor, I is importance class and K is

the behavior/structural performance factor.

Figure 4-10 - Design spectrum after NBC 105 [20]

Design force can then be obtained either through lateral force- or response spectrum analysis. Both

are to be analyzed by the same approach as for IS1893.

4.3.4 Drift limits

All deformations from linear elastic analysis is to be multiplied by a factor of 5/K. For all

structures, the drift limit is set to 1% and should not exceed 60mm.


Thomas Ødegaard 54

4.4 Performance based seismic design

With regards to performance based seismic design, the following regulations and guidelines are

considered:

• ASCE 41-13 – Seismic Evaluation and Retrofit of Existing Buildings [21]

• FEMA 356 – Pre-standard and Commentary for the Seismic Rehabilitation of Buildings

[22]

The main gist of the performance-based seismic design methodology is to determine the structural

performance of a structure in accordance with earthquake of different magnitude.

Table 4-8 - PBSD after FEMA 356 with example acceptance criteria

Target building Performance Level

Operational Immediate

Occupancy

Life Safety Collapse

Prevention

Ear

thquak

e H

azar

d

Lev

el

50%/50year

20%/50year

10%/50year

2%/50year

This design philosophy is incorporated into many building codes to a higher or lower degree. In

Eurocode 8-1, for design of new buildings, there are defined two performance levels; Damage

Limitation and Collapse Prevention. In Eurocode 8-3, for evaluation of existing buildings, a third

performance level is introduced; Significant Damage.

Table 4-9 - Approximation of performance levels of ASCE 41-13 and EC8-3

ASCE 41-13 Operational Immediate occupancy Life safety Collapse prevention

EC8-3 Damage limitation Significant damage Near Collapse


The definition of seismic hazard levels is not uniform across the codes. FEMA 356 describes four

seismic hazard levels, depended on maximum earthquake probabilities. In the case study of this

thesis it is chosen to analyze for earthquakes with 50%-, 10%- and 2% probability of occurrence

in 50 years.

4.4.2 Performance levels

The performance level is limit states that describes the integrity of a structure. There are many

ways in which performance levels are defined, but a common definition used is; Opertaional (O),

Immediate occupancy (IO), Life safety (LS) and Near collapse (NC). Per ASCE 41-13 the

description of the performance levels are as follows:


Thomas Ødegaard 55

Tabell 2 - Decription of performance levels4

Performance Levels

(Structural system) Description

S-1 – Immediate Occupancy

(IO)

“Immediate Occupancy is the post-earthquake damage state in which only very limited

structural damage has occurred. The basic vertical- and lateral-force-resisting systems of the

building retain almost all of their pre-earthquake strength and stiffness. The risk of life-

threatening injury as a result of structural damage is very low, and although some minor

structural repairs might be appropriate, these repairs would generally not be required before

re-occupancy. Continued use of the building is not limited by its structural condition but

might be limited by damage or disruption to nonstructural elements of the building,

furnishings, or equipment and availability of external utility services.”

S-2 – Damage Control “Damage Control, is defined as a post-earthquake damage state between the Life Safety

Structural Performance Level (S-3) and the Immediate Occupancy Structural Performance

Level (S-1).”

S-3 – Life safety (LS) “Life Safety, is defined as the post-earthquake damage state in which a structure has damaged

components but retains a margin against the onset of partial or total collapse.”

S-4 – Limited safety “Limited safety is defined as a post-earthquake damage state between the Life Safety

Structural Performance Level (S-3) and the Collapse Prevention Structural Performance

Level (S-5).”

S-5 – Collapse Prevention (CP) “Collapse prevention is defined as the post-earthquake damage state in which a structure has

damaged components and continues to support gravity loads but retains no margin against

collapse.”

S-6 – Not considered “Where an evaluation or retrofit does not address the structure, the Structural Performance

Level shall be Structural Performance Not Considered (S-6).”

Performance Level –

Nonstructural components Description

N-A – Operational “Nonstructural Performance Level N-A is the post-earthquake damage state in which the

nonstructural components are able to provide the functions they provided in the building

before the earthquake.”

N-B – Position Retention “Nonstructural Performance Level N-B is the post-earthquake damage state in which

nonstructural components might be damaged to the extent that they cannot immediately

function but are secured in place so that damage caused by falling, toppling, or breaking of

utility connections is avoided. “

N-C – Life Safety “Nonstructural Performance Level N-C is the post-earthquake damage state in which

nonstructural components may be damaged, but the consequential damage does not pose a

life-safety threat”

N-D – Not considered “Where an evaluation or retrofit does not address all nonstructural components to one of the

levels in the previous sections, the Nonstructural Performance Level shall be Nonstructural

Performance Not Considered (N-D).”


Thomas Ødegaard 56

With a combination of these the following building performance levels are defined:

Building Performance Level Description

1-A – Operational Backup utility services maintain function; very little

damage (S-1 & N-A).

1-B – Immediate Occupancy The building remains safe to occupy; any repairs are

minor (S-1 & N-B)

3-C – Life Safety Structure remains stable and has significant reserve

capacity; hazardous damage is controlled (S-3 & N-C)

5-E Collapse Prevention The building remains standing, but only barely; any

other damage or loss is acceptable (S-5 & N-E)

4.4.3 Acceptance criteria

There are a lot of different answers as to what parameters of the analysis that will predict the

performance level. The limit state set for each performance level is referred to as “acceptance

criteria”. This section will present the most used

4.4.3.1 Interstory drifts, velocity and acceleration

The interstory drift is a good indicator of the performance level of a structure. It is easily defined

as the ratio of displacement of two adjacent floors, divided on the floor height. Usually analyzed

in both x-, y- direction:

𝑑𝐼 =𝑢𝑓𝑙𝑜𝑜𝑟 𝑖 − 𝑢𝑓𝑙𝑜𝑜𝑟 𝑖−1

𝐻𝑓𝑙𝑜𝑜𝑟= % (4.30)

Transient drift ratio is defined as the maximum resultant interstory drift:

𝑑𝐼,𝑇 = √𝑑𝐼,𝑥2 + 𝑑𝐼,𝑦

2 (4.31)

With regards to defining acceptance criteria with drift demands, there is no consensus on what

these limits should be. FEMA 356 presents suggested drift limits for the different performance

levels, which are used in the case study. With this in mind, the use of drift limits as acceptance

criteria on its own is not enough to define the true performance of the building and should be

accompanied by other acceptance criteria.

4.4.3.2 Plastic hinge rotation

The acceptance criteria for plastic hinge rotation of beams and columns can be found in table 10-

7 and 10-8 in ASCE 41-13.

For beams controlled by flexure, the acceptance criteria depend on the balance of compression and

tension rebar in the beam, conformity of transverse reinforcement, shear force at hinge location.

For columns controlled by flexure, the acceptance criteria depend on the axial force ratio of the

columns.


Thomas Ødegaard 57

4.4.4 Analysis

The perform the seismic performance assessment, several analysis methods can be used.

If the structure is expected to behave linearly, most relevant for earthquakes of 50% in 50 years,

linear analysis can be conducted. Here both response spectrum and linear time history analysis can

be used, with minor limitation for response spectrum analysis for structures of high complexity. If

the other earthquake hazard levels are to be analyzed by time history analysis, then the ground

motions can easily be scaled the desired hazard level.

If the structure is expected to behave nonlinearly, which would most likely be the case for

earthquakes of 10-2% probability of occurrence in 50 years, either nonlinear static- or nonlinear

time history can be used to determine structural performance. ASCE 41-13 does allow for linear

analysis approaches nonlinearly behaving structures, but the most accurate approach would be to

use nonlinear analysis methods.


Thomas Ødegaard 58

5 CASE STUDY

Kanti Children’s hospital is situated in the north-eastern part of Kathmandu, Nepal. There is

planned an extension to make room for a child-psychiatrics department. The extension is to be

built as a separate building on the western part of the hospital site.

Figure 5-1 – North-elevation view (Ref. Team Consultants)

The building is planned with 4 stories of 492m2. The structural system consists of concrete moment

resisting frames, shear walls, and floor slabs. In the facade there is infill brick walls.

A geotechnical report was conducted for the hospital site. This report concludes that there is no

risk of liquefaction, as the waterbed is found to be deeper than 15m. Four standard penetration

tests were conducted, with equivalent SPT values at the surface layer ranging from 14-29. There

was proposed to use a piled-raft system as the foundation of the building.

The proposed structural design is based on provision from IS1893, and consists of the following

column-, beam- and shear wall plan:

Figure 5-3 – Beam- and column plan for story 1-4

Figure 5-2 - Site plan, Kanti Children’s hospital


Thomas Ødegaard 59

Figure 5-4 - Shear wall configuration

X-axis

Y-a

xis


Thomas Ødegaard 60

The following sections were used in the analytical model:

For all concrete sections, a 40mm cover is assigned.

Table 5-1 - Beam sections

Beam ID: AT-1 AT-2 AT-3 AT-4 AT-5 AT-6 AT-7 AT-8 AT-9 AT-10 AT-11 AT-12

Width [mm] 270 270 300 300 300 300 300 300 300 300 300 270

Depth [mm] 400 400 500 500 500 500 500 500 500 500 500 400

Rebar

tension

3xØ16 3xØ16 1xØ16

2xØ20

1xØ16

2xØ20

1xØ16

2xØ20

1xØ16

2xØ20

2xØ16

2xØ20

1xØ16

2xØ20

1xØ16

3xØ20

1xØ16

2xØ20

1xØ16

2xØ20

1xØ12

2xØ16

Area [mm2] 603 603 829 829 829 829 1030 829 1143 1143 1143 515

Rebar

compression

4xØ16 2xØ16 3xØ16

2xØ20

2xØ20 2xØ16

2xØ20

3xØ16

3xØ20

3xØ20 3xØ20 4xØ16

3xØ20

2xØ16

3xØ20

4xØ16

3xØ20

3xØ20

Area [mm2] 803 402 1231 628 1030 1545 942 942 1746 1344 1746 942

Table 5-2 - Column sections

Column ID

[500x500mm]

C1

C2

C3

C4

C5

Rebar configuration 8xØ12

8xØ16

16xØ16 8xØ20

8xØ16

12xØ20

4xØ16

8xØ20

8xØ25

Area [mm2] 2512 3215 4120 4572 6437

Table 5-3 - Slab sections

Slabs: Thickness [mm] Long. rebar Vert. rebar

Shear walls 230 Ø10/cc150mm

533mm/m

Ø12/cc150mm

753mm/m

Floor slabs 200 Not set/not relevant Not set/not relevant


Thomas Ødegaard 61

5.1 Structural analysis Model

A spatial model was created in SAP2000 based on the initial structural design. Beams and columns

were modeled as line elements, floor- and stairway slabs were modeled as thin shell elements, and

shear walls were modelled as nonlinear-layered shell elements.

The base of the structural model is assumed fixed constrained. This was done as the foundation

consists of a piled raft system, providing moment retention, and since neither IS1893 or Eurocode

requires implementation of soil-structure-interaction. For the geotechnical properties of the site,

implementation of SSI would most likely provide more liberal results, making it a conservative

assumption.

Figure 5-5 - Structural analysis model

Figure 5-6 - Shear wall configuration


Thomas Ødegaard 62

For all structural members, concrete of class M20 and rebar of quality HYSD500 is used:

Table 5-4 - Material properties

Materials

Characteristic

strength [MPa]

Modulus of

elasticity [MPa]

Poisson ratio

[𝝂] Weight

[𝒌𝑵/𝒎𝟑]

Concrete - M20 20 22 360 0.3 25

Rebar – HYSD500 500 200 000 0.2 77

The shear walls were modeled as nonlinear layered shell elements. The mesh size was configured

to be maximum 800x800mm. The shear walls have the following configuration:

Table 5-5 - Shear wall configuration

Type Thickness 𝝈𝒙 𝝈𝒚 𝝈𝒙𝒚

Concrete Membrane 230mm NL NL NL

Rebar Top Vert. Membrane 0.753mm NL - NL

Rebar Top Hor. Membrane 0.753mm NL - NL

Rebar Bot. Vert. Membrane 0.753mm NL - NL

Rebar Bot. Hor. Membrane 0.753mm NL - NL

Center of mass and rigidity is calculated after procedures presented in chapter 3.5.

Figure 5-7 - Center of mass- and rigidity, and radius of gyration for main floors and mumty


Thomas Ødegaard 63

As the loading schemes according to EC8 and IS1893 were quite similar, calculations for torsional

radii were conducted for EC8-model, but deemed applicable for IS1893-model:

Table 5-6 - Torsional parameters

Center of mass

[mm]

Eccentricity

[mm]

Torsional radius

[mm]

Radius of gyration

[mm]

x y 𝑒0𝑥 𝑒0𝑦 𝑒0 𝑟𝑥 𝑟𝑦 𝑙𝑠

Story 2- Roof 8 067 12 030 798 820 1144 11 707 9 946 1 417

Mumty 4 700 20 300 333 935 993 5 339 6 116 1 461

Rigid diaphragm constraints were assigned to all nodes connected to the floor slabs at each story.

This is applicable for both EC8 and IS1893 as the depth of the floor slabs is sufficient. The floor

mesh size was set to maximum 800x800mm to properly include the interaction between the slab

and beams.

Figure 5-8 - Diaphragm constrains. Left side. floor 1-roof, right side: mumty

As the differences regarding loading and effective stiffness yield quite similar results in a modal

analysis, only the modal analysis for EC8 is presented.

A total of 450 modes were used in the analysis, achieving modal load participation of

[𝑢𝑥, 𝑢𝑦, 𝑢𝑧] ≈ 100%. The four first, and most prominent modes are:


Thomas Ødegaard 64

Table 5-7 - Modal mass participation

Modal mass participation ratio

Mode Period [s] Ux Uy Rz

1 0.43 0% 46% 23%

2 0.33 61% 0% 4%

3 0.30 0% 22% 30%

4 0.22 7% 0% 10%

Where Ux and Uy is displacement in x-, y-direction and Rz is torsional rotation.

From the results it can be seen that is a significant torsional effect on this building. This is to be

expected due its irregular plan structure. The modal analysis also indicates that the mumty seems

to be the most fragile part of the structural design.


Thomas Ødegaard 65

Figure 5-9 - First four mode shapes in ascending order. Color-coding show resultant displacement.


Thomas Ødegaard 66

As the behavior of the stairway seems to be of great significance regarding the structural reliability,

the inter-story drift calculated in the following chapters are calculated for both the gravity center

and corner of the stairway.

For the nonlinear analysis model some changes were made to account for nonlinearity and to

improve computational efficiency.

Table 5-8 - Changes to analysis model for nonlinear behavior

Pushover Time History

Column hinges Fiber P-M2-M3 Fiber P-M2-M3

Primary beam hinges M3-Hinges (Auto ASCE 41-13) Fiber P-M2-M3

Secondary beam hinges M3-Hinges (Auto ASCE 41-13) No hinge assigned

Shear wall No additional meshing No additional meshing

For the direct integration time-history analysis, the rebar configurations of the columns in the

stairway was increased. This is further discussed in Chapter 5.4.3

Figure 5-10 - Location of nodes for calculation of inter-story drift. L.S Stairway, R.S. gravity center


Thomas Ødegaard 67

5.2 EC8

The building is regular in elevation while irregular in plan, so a spatial analytical model is required.

The original design considered a high degree of ductility due to a dual frame-, and shear wall

system. In a comparative study of code provisions for ductile reinforce concrete structures [23],

the highest ductility category for dual frames after IS1893 (SMRF) was seen to approximate the

ductility category DCM in Eurocode 8. The structure is therefor set to follow the criteria of DCM.

Values for peak ground acceleration were obtained from the conference paper “Comparative study

of seismic hazard of Kathmandu valley, Nepal with other seismic prone cities” [9]. The seismic

hazard described in this paper is based probabilistic seismic hazard analysis, were the level of

seismicity and obtained PGA is comparative to cities such as Sendai, Japan and Los Angeles, USA.

The following design parameters were used in the analysis:

Table 5-9 - Seismic design parameters - EC8

Peak ground acceleration (95-year return) 0,26 [g]



Design vertical ground motion 0.9𝑎𝑔

Ground type: [24] C

Soil factor (S) 1,15

Tb(s) 0,2 [s]

Tc(s) 0,6 [s]

Td(s) 2 [s]

Damping 5%

Importance factor IV 1,4

The design ground accelerations are then calculated as:

𝑎𝑔,𝑁𝑜 𝐶𝑜𝑙𝑙𝑎𝑝𝑠𝑒 = 1.4 ⋅ 𝑎𝑔,475 = 0.69𝑔 (5.1)

𝑎𝑔,𝐷𝑎𝑚𝑎𝑔𝑒 𝐿𝑖𝑚𝑖𝑡𝑎𝑡𝑖𝑜𝑛 = 1.4 ⋅ 𝑎𝑔,475 = 0.36𝑔 (5.2)

Dead loads obtained from the architectural design, and imposed loads according to EC8 are as

follows:

Table 5-10 – Characteristic loads - EC8

Dead loads Floor finishing and partitions 2,5 kN/m2

Brick walls (350x3650mm) 19 kN/m

Imposed Loads

Rooms 2 kN/m2

Stairways and passages 4 kN/m2

Accessible roof 1,5 kN/m2

Inaccessible roof 0,75 kN/m2


Thomas Ødegaard 68

For the imposed loads a quasi-permanent load factor is assigned:

𝜓𝐸,𝑓𝑙𝑜𝑜𝑟 = 𝜓2,𝑓𝑙𝑜𝑜𝑟 ⋅ 𝜑𝑓𝑙𝑜𝑜𝑟 = 0.15

𝜓𝐸,𝑟𝑜𝑜𝑓 = 𝜓2,𝑟𝑜𝑜𝑓 ⋅ 𝜑𝑟𝑜𝑜𝑓 = 0.28 (5.3)

The seismic weight considered in all seismic analysis is then:

∑𝐺𝑘,𝑖 + ∑(𝜓𝐸,𝑖 ⋅ 𝑄𝑘,𝑖) (5.4)

For the damage limitation demand, the following limits are set:

Table 5-11 - Drift limits, Damage limitation

Nonstructural component Drift limit

Brittle 0.5%

Ductile 0.75%

Non-interfering 1%


Thomas Ødegaard 69


The process of determination of the behavior factor was done in two parts. First the initial behavior

factor was determined by the regulations in the code. After a preliminary response spectrum

analysis, with the initial behavior factor, a pushover analysis was performed to modify the behavior

factor.

5.2.1.1 Initial behavior factor:

The building is deemed irregular in plan and regular in elevation. The building is set to satisfy

DCM. The structure is classified as a dual frame system, as it is a combination of columns for

vertical loads, and shear walls to resist the majority of the lateral loads.

First, an elastic lateral force analysis is performed to determine if the dual structural system is

classified as frame- or wall-equivalent. In a preliminary analysis it was determined how much of

the base shear that was obtained by the shear walls:

𝑉𝑤𝑎𝑙𝑙,𝑥

𝑉𝑏,𝑥=

8 821𝑘𝑁

10 759𝑘𝑁= 82% (5.5)

𝑉𝑤𝑎𝑙𝑙,𝑦

𝑉𝑏,𝑦=

8 336𝑘𝑁

10 759𝑘𝑁= 77% (5.6)

As more than half the total base shear is sustained by the shear walls, the structural system is

classified as a wall-equivalent dual system. Per clause 4.3.6.1 (4) the interaction of masonry infills

can then also be neglected.

Furthermore, it is investigated if the structure is classified as torsional rigid, according to clause

5.2.2.1 (4).

Table 5-12 - Evaluation of torsional effect

Eccentricity

[mm]

Torsional radius

[mm]

Radius of

gyration

[mm]

𝑒0𝑥 𝑒0𝑦 0.3𝑟𝑥 0.3𝑟𝑦 𝑟𝑥 𝑟𝑦 𝑙𝑠

Story 2-

Roof

798 820 3 512 2 984 11 707 9 946 1 417

Mumty 333 935 1 601 1 850 5 339 6 116 1 461

After the following relations, it is determined that the structural system is torsional rigid:

[𝑒0𝑥, 𝑒0𝑦] ≤ 0.3[𝑟𝑥, 𝑟𝑦] (5.7)

𝑙𝑠 ≤ [𝑟𝑥, 𝑟𝑦] (5.8)

With this classification set, the factor kw is set after clause 5.2.2.2 (11), where 𝛼0 is the prevailing

aspect ratio of the walls in the structural system.

𝛼0,𝑥 =3 ⋅ 14.6𝑚

2 ⋅ 3.5 + 4.66= 3.76 ≥ 2 (5.9)


Thomas Ødegaard 70

𝛼0,𝑦 =5 ⋅ 14.6𝑚

4 ⋅ 3.5 + 7= 3.91 ≥ 2 (5.10)

𝑘𝑤,𝑥 = 1 (5.11)

𝑘𝑤,𝑦 = 1 (5.12)

The initial behavior factor is thereby set to:

𝑞 = 𝑞0(= 3) ⋅ (1 + 1.2

2) ⋅ 𝑘𝑤 = 3.3 (5.13)

After a pushover analysis is performed, see chapter 5.2.3, the behavior factor is modified.

𝑞 = 𝑞0(= 3) ⋅ 1.5 ⋅ 𝑘𝑤 = 4.5

(5.14)


Thomas Ødegaard 71


For linear-elastic analysis the effective stiffness (cracked concrete) is reduced from the gross

stiffness due to the hysteretic loading effect that earthquakes yield, according to clause 4.3.1(7).

The torsional stiffness is reduced per recommendations in the book “Seismic Design of Concrete

Buildings to Eurocode 8” [18].

Table 5-13 - Cracked concrete stiffness

Effective moment of inertia – column 50% of uncracked

Effective moment of inertia – beam 50% of uncracked

Effective torsional stiffness 10% of uncracked

The linear elastic analyses follow the procedure of appendix B-1:.

The lateral force method is applied for the first mode in the x-y- direction. The modes are obtained

by modal analysis of the structure, as the model is already prepared for more detailed analysis.

To achieve a modal load participation ratio of 90% for x-, y- and z- direction a total of 450 modes

were used in the response history analysis.

For all linear analysis, horizontal directional values are calculated as:

𝐸𝐸𝑑𝑥 ± 0.3𝐸𝐸𝑑𝑦 (5.15)

𝐸𝐸𝑑𝑦 ± 0.3𝐸𝐸𝑑𝑥 (5.16)

Results from initial lateral force- and response spectra analysis with behavior factor 𝑞 = 3.3.

Table 5-14 - Initial response spectrum analysis

Z

[m]

Seismic

weight

[kN]

Response spectrum - X Response spectrum – Y

𝑭𝒙 𝑭𝒚 𝑭𝒙 𝑭𝒚

Mumty 18.25 550 748 419 648 563

Roof 14.6 6 045 5 389 2 061 2 085 4 681

4 10.95 7 625 8 679 2 937 3 155 7 337

3 7.3 7 625 10 587 3 606 3 876 9 078

2 3.65 7 625 11 646 4 118 4 579 10 109

Sum/base 0 29 470 11 646 4 118 4 579 10 109


Thomas Ødegaard 72

After the pushover analysis was conducted the behavior factor was increased to 𝑞 = 4.5. As the

main mode of vibration for x-, y-direction yields the same spectral acceleration, the results for

lateral force method will be equal in both directions.

Figure 5-11 - Design response spectrum - Eurocode 8

Table 5-15 - Response spectrum analysis - modified behavior factor

Z

[m]

Seismic

weight

[kN]

L.F [kN] R.S.-X [kN] R.S.-Y [kN]

X/Y Y/X X Y X Y

Mumty 18.25 1 009 373 118 566 330 167 491

Roof 14.6 5 559 4 341 1 325 4 102 1 617 3 557 1 673

Story 4 10.95 7 636 7 562 2 280 6 473 2 230 5 457 2 424

Story 3 7.3 7 636 9 699 2 919 7 949 2 728 6 747 3 028

Story 2 3.65 7 636 10 965 3 289 8 876 3 212 7 636 3 539

Sum/Base 0 29 476 10 965 3 289 8 876 3 212 7 636 3 539


Thomas Ødegaard 73

With both the peak ground acceleration of 50% and 10% probability of occurrence available, the

reduction factor to transform the drifts can be calculated directly.

𝜈 =𝑎𝑔,475

𝑎𝑔,95= 0.53 (5.17)

This is higher than the recommended values from the Eurocode, which can be explained by the

abnormal seismicity of the region in question.

Table 5-16 - Drift limits - Damage limitation

𝒅𝑰

𝑯𝒊≤

𝟎. 𝟓%

𝟎. 𝟓𝟑= 𝟎. 𝟗𝟒% Structures with brittle non-structural elements

𝒅𝑰

𝑯𝒊≤

𝟎. 𝟕𝟓%

𝟎. 𝟓𝟑= 𝟏. 𝟒𝟏% Structures with ductile non-structural elements

𝒅𝑰

𝑯𝒊≤

𝟏%

𝟎. 𝟓𝟑= 𝟏. 𝟖𝟖% Structures with non-interfering non-structural elements

The inter-story drift was calculated for both the gravity center and the stairway and the corner

stairway with locations presented in Figure 5-10 - Location of nodes for calculation of inter-story

drift.


Thomas Ødegaard 74

Figure 5-12 - Interstory drifts at gravity center

Figure 5-13 - Interstory drifts at stairway

The main building is just within the requirements of damage limitation for structures with brittle

nonstructural components. The stairway on the other hand does not fulfill these requirements, with

the most unfavorable results obtained from the response spectrum analysis.

These analyses also exemplify the difference of the lateral force- and response spectrum analysis

methods. Even though the structure fulfills the requirements for use of lateral force method, and

said analysis yields a significantly higher base shear, the response spectrum analysis yields a more

conservative result with regards to torsional displacements.

Ultimately, the structure does not fulfill the damage limitation demand of Eurocode 8.


Thomas Ødegaard 75

5.2.3 Non-linear Static Analysis

Plastic hinges were manually assigned to all locations with possibility of plastic hinge formation.

For this analysis fiber hinges were assigned to all columns, and M3 hinges to all beams following

table 10-7 of ASCE 41-13. In SAP2000 the hinges following ASCE 41-13 has the possibly to

display graphically the hinge state, making it very easy to determine the first yield point (as the

first yield most likely occur in the beams) for the over-strength factor.

The analysis follows the N2-method (Fajfar 2000) presented Annex B in EC8, and the analysis

procedure is presented in appendix B-2:.

As the pushover analysis is mostly suited for regular buildings with regular mode shapes. It is

therefore chosen to use the pushover analysis to determine the response of the main structure and

including the mumty into the roof-level. The story shear and inter-story drift is though displayed

for the target displacements.

To perform the pushover analysis, two load cases were generated in SAP2000. To each load case

a lateral acceleration load was introduced. The load was set to increase incrementally until a target

displacement in the control node was reached. The control nodes were assigned at the center-edges

of the roof-level. P-delta effects were also accounted for.

The target displacement was set way beyond what was expected of the structure to resist, to capture

the full behavior of the structure. As the structural model is quite complex, the degradation after

peak base force was not captured well by the analysis. The range captured though is sufficient for

analysis with the given structural demand.

Figure 5-14 -Pushover curve


Thomas Ødegaard 76

The displacement shape is derived from the linear part of the pushover analysis:

Table 5-17 - Displacement shape

𝚽𝒙 𝚽𝒚 Seismic weight

[kg]

Roof 1 1 670 521

Level 4 0.70 0.73 778 389

Level 3 0.41 0.45 778 389

Level 2 0.15 0.17 788 389

The transformation factor is established:

Γx =∑𝑚𝑖Φ𝑖

∑𝑚𝑖Φ𝑖2 = 1.376 (5.18)

𝑚𝑥∗ = ∑𝑚𝑖Φ𝑖 = 15 191𝑘𝑁 (5.19)

The location of the plastic mechanism “A” is determined graphically from the idealized pushover

curve.

Figure 5-15 - Idealized pushover curves

Further, calculations followed the steps in Chapter 4.1.6.1. The following target displacements and

design parameters were obtained:

Table 5-18 - Target displacements – Pushover analysis

d[mm] Fbase [kN]

𝒅𝒕,𝒙,𝒏𝒐 𝒄𝒐𝒍𝒍𝒂𝒑𝒔𝒆 80 39 180

𝒅𝒕,𝒙,𝒅𝒂𝒎𝒂𝒈𝒆 𝒍𝒊𝒎𝒊𝒕𝒂𝒕𝒊𝒐𝒏 42 25 218

𝒅𝒕,𝒚,𝒏𝒐 𝒄𝒐𝒍𝒍𝒂𝒑𝒔𝒆 86 37 842

𝒅𝒕,𝒚,𝒅𝒂𝒎𝒂𝒈𝒆 𝒍𝒊𝒎𝒊𝒕𝒂𝒕𝒊𝒐𝒏 39 24 179


Thomas Ødegaard 77

Figure 5-16 - Target displacements in x-, y-direction

At the target displacements, design parameters such as inter-story drifts and story shear forces

were obtained:

Figure 5-17 - Inter-story drifts at target displacements


Thomas Ødegaard 78

Table 5-19 - Design values from pushover analysis

Damage limitation Collapse Prevention

Pushover X Pushover Y Pushover X Pushover Y

Drift [%] Vx

[kN]

Drift [%] Vy

[kN]

Drift [%] Vx

[kN]

Drift [%] Vy

[kN] Center Stair Center Stair Center Stair Center Stair

Mumty 0.39% 0.37% 388 1.45% 0.27% 355 1.06% 0.70% 649 3.23% 0.47% 892

Roof 0.32% 0.34% 5 812 1.14% 0.22% 5 477 0.58% 0.64% 9 131 2.16% 0.42% 8 276

Level 4 0.32% 0.24% 11 679 0.81% 0.23% 11 237 0.60% 0.43% 18 221 1.55% 0.46% 17 283

Level 3 0.30% 0.24% 17 562 0.48% 0.22% 17 061 0.58% 0.46% 27 309 0.92% 0.45% 26 336

Level 2 0.17% 0.20% 25 218 0.17% 0.14% 24 179 0.32% 0.36% 39 180 0.32% 0.27% 37 842

Base 0% 0% 25 218 0% 0% 24 179 0% 0% 39 180 0% 0% 37 842

Figure 5-18 - Resultant displacements [mm] – Pushover X. l.s. “Damage limitation”, r.s. “No collapse”

Figure 5-19 - Resultant displacements [mm] – Pushover Y. l.s. “Damage limitation”, r.s. “No collapse”.


Thomas Ødegaard 79

Results from the pushover analysis confirms the results from the linear-elastic analysis. The main

building complies with the damage limitation requirements, while the stairway does not. The

interstory of the stairway with no collapse seismic hazard is significant. As the pushover analysis

has some limitations regarding torsional effects, the results from this analysis should be considered

as liberal.

The over-strength value is calculated after clause 5.2.2.2 (3). 𝛼1 is in this case determined by the

base shear that first induces a structural member to yield, while 𝛼1is determined graphically by the

first peak in the pushover curve.

Figure 5-20 - Values for determination of over-strength factor

Table 5-20 - Calculated overstrength factor

X Y

Shear force – first yield [kN] 15 300 15 725

Shear force – fully plastic [kN] 45 000 36 000

𝜶𝒖

𝜶𝟏≤ 𝟏. 𝟓

2.94 2.29

𝜶𝒖

𝜶𝟏 1.5

The over-strength factor is further used to modify the behavior factor, which is used in all linear

elastic analysis.

Full calculations can be found in appendix C-1:.


Thomas Ødegaard 80

5.3 IS1893

For the analysis following IS1893, the following assumptions and requirements are made:

• The lateral load resisting system is classified as ductile RC structural walls with RC

SMRFs. Structural detailing of the reinforced concrete must comply with IS 456 [25] and

IS 13920 [19].

• Seismic zone factor for Nepal, equivalent to Zone V in IS1893. This was used in the

proposed structural design and considered “common practice”.

The analysis process follows mainly the same steps as the linear-elastic analysis for Eurocode in

chapter 5.2.

Table 5-21 - Seismic design parameters - IS1893

Seismic Zone (Z): V 0,36

Ground type: [24] II

Damping 5%

Importance factor 1,5

Behavior factor 5

For the loading scheme, the same dead loads as defined for Eurocode 8 is used, while imposed

loads have been obtained from IS 875 [26].

Table 5-22 - Loading scheme – IS1893

Dead loads Floor finishing and partitions 2.5 kN/m2

Brick walls (270x3650mm) 19 kN/m

Live Loads

Rooms 2 kN/m2

Stairways and passages 4 kN/m2

Accessible roof 1.5 kN/m2

Inaccessible roof 0.75 kN/m2

The seismic weight of the building is comprised of; characteristic dead loads, 25% of live loads

less or equal to 3kN/m2, and 50% of imposed loads over 3kN/m2.


Thomas Ødegaard 81

Table 5-23 - Seismic weight after IS1893

Weight [kN]

Story 2 7 636

Story 3 7 636

Story 4 7 635

Roof 6 058

Mumty 508

Full seismic weight 29 930

Per clause 6.4.31 the moment of inertia for the columns and beams are reduced to the cracked

moment of inertia. As with the linear elastic analysis after Eurocode 8, the effective torsional

stiffness is also reduced.

Table 5-24 - Cracked concrete stiffness

Effective moment of inertia – column 70% of uncracked

Effective moment of inertia – beam 35% of uncracked

Effective torsional stiffness 10% of uncracked

The building is classified as irregular in plane, and regular in elevation. From the modal analysis,

the criteria defined in chapter 4.2.2.3. The three first modes yields a modal mass participation of

[𝑀𝑥, 𝑀𝑦] = [61%, 68%], and so does not comply with the criteria. The difference between the

two first modes are 0.33𝑠 ≥ 0.9 ⋅ 0.43 = 0.39𝑠, and so does comply with the criteria.

5.3.1 Lateral force method

The linear elastic analyses follow the procedure of appendix B-1:, with some configurations to

comply with IS1893.

The first modes in x-, y-direction are within the range [0.1s, 0.55s], so the seismic design factors

are calculated as:

𝐴ℎ,𝑥(0.42) = 𝐴ℎ,𝑦(0.34) =(𝑍2) (

𝑆𝑎

𝑔 )

(𝑅𝐼 )

= 0.135 (5.20)

𝐴𝑣 =(23) (

𝑍2)2.5

RI

= 0.09 (5.21)

The total base shear is then calculated by the following:

𝑉𝐵 = 𝐴𝑉 ⋅ 𝑊𝑠𝑒𝑖𝑠𝑚𝑖𝑐 (5.22)


Thomas Ødegaard 82

Table 5-25 - Base shears - Lateral force method

Ah W [kN] Base shear [kN]

X-direction 0.135

29 963

3 932

Y-direction 0.135 3 932

Z-direction 0.09 2 697

Further, the base shear is distributed to the floors with a linear pattern after the following formula:

𝑄𝑖 = (𝑊𝑖ℎ𝑖

2

∑(𝑊𝑖ℎ𝑖2)

)𝑉𝐵

(5.23)

Table 5-26 - Design lateral loads - Lateral force method

Z

[m]

Weight

[kN]

VB

[%]

Gi

[kN]

Vi

[kN]

Mumty 18.25 508 6% 228 228

4 14.6 6 058 44% 1 742 1 970

3 10.95 7 799 32% 1 261 3 231

2 7.3 7 799 14% 561 3 792

1 3.65 7 799 4% 140 3 932

Sum/Base 29 963 100% 3 932 3 932

The design shear force is further used to scale the horizontal design spectrum for the response

spectrum analysis.


Thomas Ødegaard 83

5.3.2 Response Spectrum analysis

With the design parameters from Table 5-21, a preliminary response spectrum analysis was

performed. The base results were the used to calculate a scaling factor, to scale the horizontal

design spectrum to provide base shears equivalent to the ones obtained by the lateral force method:

Table 5-27 - Scaling of response spectrum

Base shear – L.F

[kN]

Base shear – R.S

[kN] VB,L.F / VB,R.S

X-direction 3 932 2 538 1.549

Y-direction 3 932 2 206 1.782

Another response spectrum analysis was then performed with increased values. From this point,

the seismic response was computed with the following combination:

𝐸𝐸𝑑𝑥 ± 0.3𝐸𝐸𝑑𝑦 (5.24)

𝐸𝐸𝑑𝑦 ± 0.3𝐸𝐸𝑑𝑥 (5.25)

Table 5-28 - Response spectrum analysis results

Z

[m]

Seismic

weight

[kN]

Response spectrum - X Response spectrum – Y

𝑭𝒙[𝒌𝑵] 𝑭𝒚[𝒌𝑵] 𝑭𝒙[𝒌𝑵] 𝑭𝒚[𝒌𝑵]

Mumty 18.25 508 264 152 224 252

Roof 14.6 6 058 1 833 786 1 894 733

4 10.95 7 799 2 960 1 138 2 968 1 111

3 7.3 7 799 3 609 1 401 3 675 1 364

2 3.65 7 799 3 965 1588 4 093 1 620

Sum/base 0 29 963 3 965 1588 4 093 1 620


Thomas Ødegaard 84

5.3.3 Deformation control

Torsional regularity must be verified, following the procedure of chapter 4.2.2.3. The

displacements are obtained from the response spectrum analysis conducted, and the least favorable

pair of deflections were selected.

Figure 5-21 - Evaluated nodes

Table 5-29 - Torsional irregularity

South West North East

∆𝒎𝒂𝒙 11.3mm 5.7mm 9.9mm 5.7mm

∆𝒎𝒊𝒏 3.8mm 2.9mm 4.4mm 2.9mm

∆𝒎𝒂𝒙

∆𝒎𝒊𝒏 3.0 1.9 2.3 1.9

These results are critical. Values of ∆𝑚𝑎𝑥

∆𝒎𝒊𝒏> 2 deems the building torsionally flexible and is thereby

not compliant, as IS1893 does not allow for torsional irregular structures.

The inter-story drift limit is set by clause 7.11.1.1, and is to be obtained by the unscaled response

spectrum analysis results:

𝑑𝑟

ℎ≤ 0.4%

(5.26)


Thomas Ødegaard 85

Figure 5-22 - Inter-story drifts, response spectrum analysis, IS1893

The structures behavior is well within the drift-limits established in IS1893.


Thomas Ødegaard 86

5.4 Time History Analysis - PBSD

For the time-history analysis seven earthquake ground motions are selected and scaled according

to the elastic horizontal spectrum after clause 3.2.2.2 in Eurocode 8. For these spectrums the

importance factor is not included in the design ground motion, and the values for 50%-, 10%- and

2% probability of occurrence in 50 years were used.

The ground motions are selected based on earthquake characteristics similar to the specific site,

and the records are matched by the first mode and response spectra. It is chosen only one ground

motion per earthquake, and in the selection process it was focused on getting variation in response

in the records

Table 5-30 - Ground motion selection criteria

Fault type Reverse + Oblique [7]

Magnitue min,max 6.5-8

Rupture distance 20-60 (far field)

Shear velocity 160-320 (soil classification)

Scaled for period of vibration [0.36s, 0.3s, 0.28s]

Seven ground motions, which fulfilled the criteria of Table 5-30, were selected from the PEER

NGA West database [16]. They were then scaled to match the period of vibrations using minimized

square error.

Table 5-31 - Selected time histories

EQ-Name Mag. Fault type Year Distance

[km]

Shear

Vel.

[m/sec]

S.F.

95year

S.F.

475year

S.F.

2475year

Loma Prieta 6.93 Reverse oblique 1989 25 215 0.82 1.55 2.28

Cape Mendocino 7.01 Reverse 1992 42 337 1.44 2.71 3.98

Northridge 6.69 Reverse 1994 59 338 1.26 2.38 3.50

Chi-Chi, Taiwan 6.62 Reverse oblique 1999 38 318 1.09 2.07 3.05

Taiwan, SMART1 7.3 Reverse 1986 56 275 1.58 2.98 4.38

Chuetsu 6.8 Reverse 2007 23 278 0.69 1.31 1.92

Iwate 6.9 Reverse 2008 32 344 1.50 2.84 4.17

Gorkha Nepal 8.1 Reverse 2015 60 - - -


Thomas Ødegaard 87

Figure 5-23 - Spectral acceleration of selected ground motions for 475- and 2475year return period

Figure 5-24 - Mean response +- SD for suite of ground motions

As direct integration time-history analysis is very computationally expensive, a further selection

was made for a suite of 3 ground motions. This included the ground motions for Cape Mendocino,

Northridge and Iwate:

Figure 5-25 - Mean response of three selected ground-motions for direct integration time-history analysis


Thomas Ødegaard 88

The three selected ground motions for direct integration time-history analysis were selected based

on the mean value in the range 0.1s to 0.4s, as this is the ranges of the modes of vibration of the

structure.

The ground motions for the Gorkha earthquake is included as a curiosity to determine the

performance of the structure in those circumstances.

Time history analysis were conducted using both FNA and direct integration. This was done as it

was first assumed that the FNA procedure available in SAP2000 would sufficiently represent the

non-linear behavior of the structure. Upon further investigation and analysis, this assumption was

considered to be incorrect. In the FNA analysis, hinge rotation is greatly underestimated, thereby

reducing inter-story drifts and increasing base forces. From investigating hinge results, it seems

that when fiber element hinges are transformed to links, the hysteretic degradation is not accounted

for. With these limitations in mind, the results are represented in thesis, as the forces and

displacements of the analysis model give insight to the behavior of the structure and as a

verification of the treatment of the suite of ground motions.

All analyses follow the procedure of the flowchart in appendix B-3:.


Thomas Ødegaard 89

5.4.1 Modal linear time-history analysis

Modal linear time-history was conducted for all seven ground motions for earthquakes with 50%

probability of occurrence in 50 years. Each ground motion was analyzed in both directions,

[N,E,V] and [E,N,V]. A total of 450 modes were considered, resulting in a modal mass

participation of 95% in all directions and rotations. It was chosen to perform a linear analysis as

the structure is expected to behave solely linearly at these seismic demands. This analysis will

therefore only be eligible for evaluating the inter-story drift acceptance criteria.

Results from this analysis can also be used for the linear elastic analysis in Eurocode 8, as the

mean spectral acceleration of the suite approximates the design response spectrum of the linear

elastic analysis. It will produce slightly conservative results for the main modes of vibration, while

the high frequency modes will not properly be represented.

Figure 5-26 - Applicability of ground motions for linear elastic analysis after Eurocode 8

The base reactions from the time-history load cases are combined with a static P-Delta analysis

for axial seismic weight. Full base-results and interstory drifts are found in annex D-1:

Table 5-32 - Base reactions for linear modal analysis

Cape Mendocino Iwate Chuetsu SMART1 Chichi Northridge Loma Prieta Mean

Base shear X [kN] 13870 10041 9732 13761 12061 12671 11991 12018

Base shear Y [kN] 9867 13214 9143 10625 9834 9697 13553 10848

Base force Z [kN] 31519 32845 31949 35062 31376 32319 34804 32839

Mx [MNm] 440 498 417 474 455 459 495 463

My [MNm] 448 396 415 423 414 419 419 419

Mz [MNm] 135 196 122 217 170 129 188 165

The small variance in the base forces verifies that the scaling of ground motions is properly

performed.


Thomas Ødegaard 90

Figure 5-27 - Interstory drifts with 50% probability of occurrence in 50 years

From the interstory drifts it can be interpreted that the core building should be fully operational

while the stairway may endure some damage.


Thomas Ødegaard 91

5.4.2 Modal nonlinear time-history analysis

FNA analysis was conducted for all seven ground motions for earthquakes of 10%- and 2%

probability of occurrence in 50 years. Each ground motion was analyses in both directions, [N,E,V]

and [E,N,V]). A total of 450 modes were considered, resulting in a modal mass participation of

95% in all directions and rotations. All non-linear hinges were converted to non-linear links with

damping proportional to the tangent stiffness of the hinge. Each FNA analysis conduction took

about 1.5 hours to complete, making it a computational efficient analysis procedure in comparison

to the direct integration approach.

The base reactions from the time-history load cases are combined with a static P-Delta analysis

for axial seismic weight. Full base-results and interstory drifts are found in annex D-2: and D-3:.

Table 5-33 - Base forces for the suite of ground motions

Cape Mendecino

Iwate Chuetsu SMART1 Chichi Northridge Loma Prieta

Mean

10% in 50 years

Base shear X [kN] 23082 23246 20234 21554 20353 21468 17745 21097

Base shear Y [kN] 17867 18980 16877 20134 22178 21107 22999 20020

Base force Z [kN] 33746 35934 33733 39644 32489 34690 38761 35571

Mx [MNm] 505 558 542 548 566 587 515 546

My [MNm] 475 490 517 517 499 517 467 497

Mz [MNm] 281 285 253 260 291 292 358 289

2% in 50 years

Base shear X [kN] 34532 32321 29478 30890 33808 31892 26851 31396

Base shear Y [kN] 27505 26353 24430 29609 32527 31170 33586 29311

Base force Z [kN] 32550 38839 35787 44053 33807 37104 43281 37917

Mx [MNm] 599 646 635 646 671 706 516 631

My [MNm] 557 683 623 617 598 632 554 609

Mz [MNm] 407 351 366 381 425 415 529 411


Thomas Ødegaard 92




Thomas Ødegaard 93

5.4.3 Direct integration nonlinear time-history analysis

For the structural model for non-linear dynamic analysis, fiber-hinges were assigned to all

columns, and primary beams. Secondary beams were not expected to behave nonlinearly,

according to results of the pushover analysis (Table 5-39).

For the time integration algorithm, the Hilber-Hughes Alpha-Taylor algorithm was used with alpha

value of -0.05. This was done to filter out extensively high frequencies in the time-histories.

Rayleigh damping was calculated with 5% damping of the two first modes after equation (3.4).

During preliminary analysis, there were some convergence errors with origin in the short

columns in the stairway tower. This could indicate structural failure in column. As these columns

are arguably the most unstable part of the structural design and with a comparatively low rebar

ratio, this would seem plausible. The rebar for these columns were therefore increased to the

maximum used in the project (6xø25 + 6xø20). This eliminated all convergence errors in the

further analysis.

For the all cases the following results were obtained:

• Peak interstory drift

• Base reactions

• Plastic rotation of critical sections


Thomas Ødegaard 94

5.4.3.1 10% probability of occurrence in 50 years

For the time history analysis for 10% probability of occurrence in 50 years three ground motions

were used. With only three ground motions used in the analyses, the least favorable results were

used to perform the assessment. Full results in Appendix D-4: and D-7:.D-7:

Table 5-34 - Base reactions with 10% probability of occurrence in 50 years

Cape Mendocino Iwate Northridge Least favorable

Base shear X [kN] 13579 21571 16725 21571

Base shear Y [kN] 15987 23285 13845 23285

Base force Z [kN] 36167 30822 35983 36167

Mx [MNm] 555 574 515 574

My [MNm] 466 497 474 497

Mz [MNm] 200 304 188 304


Table 5-35 - Hinge performance with 10% probability of occurrence in 50 years

Least favorable

O IO LS NC

Column 193 5 0 0

Prim. Beam 404 6 0 0


Thomas Ødegaard 95

5.4.3.2 2% probability of occurrence in 50 years

For the time history analysis for 2% probability of occurrence in 50 years three ground motions

were used. With all seven ground motions were used in the analysis, the mean results were used

in the performance assessment. Full results in Appendix D-5: below and D-8: below. The results

from this analysis can also be used for the No collapse requirements in the Eurocode. This is

possible because the Eurocode includes the importance factor in the seismic demand.

Figure 5-31 - Applicability of ground motions for No collapse requirement after Eurocode 8

Table 5-36 - Base reactions with 2% probability of occurrence in 50 years


Base shear X [kN] 21875 29404 19289 28831 19288 19258 31369 24188

Base shear Y [kN] 22681 25279 22570 21484 22570 19145 29222 23279

Base force Z [kN] 39504 54942 40831 61336 40831 39209 47957 46373

Mx [MNm] 644 958 675 1142 675 623 845 795

My [MNm] 529 584 465 645 464 518 602 544

Mz [MNm] 271 361 300 518 304 247 400 343


Thomas Ødegaard 96


Table 5-37 - Hinge performance with 2% probability of occurrence in 50 years

Least favorable

O IO LS CP

Column 157 38 0 3

Prim. Beam 396 10 4 0

The instances of CP column hinge performance occurred in the stairway columns in the Smart1

and Loma Prieta earthquake analyses. For all three cases this was due to the


Thomas Ødegaard 97

5.4.3.3 Gorkha Earthquake

As a curiosity, the seismic performance was assessed for the Gorkha earthquake in Nepal. The

earthquake occurred in April 2015 and had a magnitude of 7.8Mw and a Mercalli Intensity of VIII.

Ground motions were obtained from Kanti Path station [27], which is located 3.5km from Kanti

Children’s Hospital, with an epicentral distance of 60km.

Figure 5-33 - Red dot: Kanti Path ground motion location. Blue dot: Kanti Childrens Hospital

Figure 5-34 - Spectral acceleration for Kanti Path ground motion


Thomas Ødegaard 98

Figure 5-35 - Kanti Path ground motions

The time history was analyzed using direct integration with HHT-value of -0.05. Rayleigh

damping was assigned, based on 5% viscous damping of the first two modes of vibration. Two

load cases were created with ground motions in N-E and E-N directions. The least favorable results

of the two were used.

Acc

eler

atio

n (

g)

Acc

eler

atio

n (

g)

Acc

eler

atio

n (

g)

Time (s)

Time (s)

Time (s)


Thomas Ødegaard 99

The following results were obtained:

Table 5-38 - Base reactions from Gorkha earthquake analysis

Base shear X [kN] 9 863

Base shear Y [kN] 8 360

Base force Z [kN] 34 095

Mx [MNm] 410

My [MNm] 393

Mz [MNm] 140

Figure 5-36 - Interstory drifts - Gorkha earthquake

The results are comparable to the linear time-history analysis with 50% probability of occurrence

in 50 years, see Figure 5-27 - Interstory drifts with 50% probability of occurrence in 50 years. This

would put the performance level for the stairway to Immediate Occupancy and Operational for the

core building.


Thomas Ødegaard 100

5.5 Pushover Analysis - PBSD

This chapter is based on the analysis performed in chapter 5.2.3. The script for the N2-pushover

analysis, with elastic response spectrum after Eurocode 8, was reused to obtain design values at

all three of the performance level. Detailed procedure is found in Appendix C-2:

Figure 5-37 - Target displacements for seismic hazard levels

Pushover X Pushover Y

Target disp.

[mm]

Base shear

[kN]

Target disp.

[mm]

Base shear

[kN]

50% in 50 years 30mm 19 663 28mm 18 634

10% in 50 years 57mm 31 254 53mm 29 773

2% in 50 years 95mm 43438 100mm 40 757

From the pushover curves in Figure 5-37 it can be interpreted that the building will not collapse

under the seismic demands set for his assessment. The pushover analysis was run until major

convergence errors halted the analysis, and its therefore unclear what the structural behavior will

be beyond the displacement of the pushover curve. For the pushover analysis in Y-direction, the

factor of safety for collapse for the largest seismic demand may be considered as being very low.



5.5.1 Interstory drifts:

Interstory drifts are calculated as transient drifts for each load case. The pushover cases are not

combined.

Figure 5-38 - Interstory drift pushover analysis, with acceptance criteria

When comparing the interstory drifts to the ones obtained from time history analysis, the shape of

the interstory drift plots (Figure 5-27, Figure 5-30 and Figure 5-32) differ quite significantly. This

is especially the case for the stairway, which is indicated to be greatly affected by torsional modes.

As torsional effects are greatly underestimated in the N2-pushover procedure, the results should

be considered as liberal, with a special concern for the results of the stairway tower.



5.5.2 Hinge results:

As noted in chapter 5.2.3, all beams were modelled using M3 hinges after ASCE 41-13. All

columns were modelled using P-M2-M3 fiber hinges. All sections were assigned hinges in both

ends. Hinge performance level was set by the acceptance criteria presented in Table 5-41.

Table 5-39 - Hinge performance levels

Pushover X Pushover Y

O IO LS CP O IO LS CP

50

% i

n

50

yea

rs

Column 198 0 0 0 198 0 0 0

Prim. Beam 410 0 0 0 410 0 0 0

Sec. Beam 240 0 0 0 240 0 0 0

10

% i

n

50

yea

rs Column 196 2 0 0 198 0 0 0

Prim. Beam 409 1 0 0 407 3 0 0

Sec. Beam 240 0 0 0 240 0 0 0

2%

in

50 y

ears

Column 170 21 7 0 182 3 13 0

Prim. Beam 400 10 0 0 399 11 0 0

Sec. Beam 240 0 0 0 240 0 0 0



5.6 Seismic performance assessment

As hospital can be considered safety critical in the event of natural disasters, it is of utmost

importance that the facilities are safe and functional under such circumstances. The proposed

performance objective is thereby set as:

Table 5-40 - Performance objective for Kanti Childrens Hospital

Operational

(O)

Immediate

Occupancy

(IO)

Life Safety

(LS)

Near Collapse

(NC)

50% in 50 years

10% in 50 years

2% in 50 years

With the high number of shear walls, and as the structural system was classified as a wall-

equivalent dual frame system per chapter 5.2.1, the acceptance criteria for interstory drift for

concrete wall systems is adopted. The following acceptance criteria is then established with basis

in ASCE 41-13 [21] and FEMA 356 [22]:

Table 5-41 - Acceptance criteria

Operational

O

Immediate Occupancy

IO

Life Safety

LS

Collapse Prevention

CP

Plastic hinge –

Beams* ≤0.005 rad 0.005 – 0.015 rad 0.015 – 0.02 rad ≥0.02 rad

Plastic hinge –

Columns Max** ≤0.005rad 0.005 – 0.045 rad 0.045 – 0.06 rad ≥0.06 rad

Plastic hinge –

Columns Min** ≤0.003rad 0.003 – 0.009 rad 0.009 – 0.06 rad ≥0.06 rad

Max interstory drift ≤ 0.5% 0.5 - 1% 1% - 2% ≥ 2%

Residual drift ≈0 0−0.5% 0.5% - 2% ≥ 2%

* The acceptance criteria based on a high shear-utilization of the beam section

** The acceptance criteria are interpolated between the min- and max-values depending on the axial utilization of the

concrete-section for each hinge.



5.6.1 Base reactions

The base reactions of the different seismic hazard level and analysis method is compared. Pushover

analyses yields the highest base reactions, which can be explained by the absence of the

implementation of torsional modes in the pushover analysis. For the modal nonlinear analyses, the

structure was assumed to be stiffer, mainly due to the definition of plastic hinges, which results in

slightly higher base reactions.

Table 5-42 - Comparison of base reaction for the different analysis methods

Linear Modal Mean

Nonlinear Modal Mean

Direct Integration

Mean

Direct Integration

Least favorable Pushover

50% probability in 50 years

Base shear X [kN] 12018 - - - 19663

Base shear Y [kN] 10848 - - - 18634

Base force Z [kN] 32839 - - - -

Mx [MNm] 463 - - - -

My [MNm] 419 - - - -

Mz [MNm] 165 - - - -

10% probability in 50 years Base shear X [kN] - 21097 - 21571 31254

Base shear Y [kN] - 20020 - 23285 29773

Base force Z [kN] - 35571 - 36167 -

Mx [MNm] - 546 - 574 -

My [MNm] - 497 - 497 -

Mz [MNm] - 289 - 304 -

2% probability in 50 years Base shear X [kN] - 31396 24188 - 43438

Base shear Y [kN] - 29311 23279 - 40757

Base force Z [kN] - 37917 46373 - -

Mx [MNm] - 631 795 - -

My [MNm] - 609 544 - -

Mz [MNm] - 411 343 - -



5.6.2 Interstory drifts

When comparing the interstory drifts there are significant differences, while the fulfillment of

acceptance criteria is very similar. As the direct integration time-history analyses are considered

as being the most accurate, these results are weighted the highest.








5.6.3 Hinge performance

Hinge performance is evaluated for both pushover- and direct integration time-history analyses.

Pushover

Direct Integration

Time-history

O IO LS CP O IO LS CP

10

% i

n

50

yea

rs Column 196 2 0 0 198 0 0 0

Prim. Beam 409 1 0 0 407 3 0 0

Sec. Beam 240 0 0 0 240 0 0 0

2%

in

50

yea

rs Column 170 21 7 0 181 5 13 0

Prim. Beam 400 10 0 0 399 11 0 0

Sec. Beam 240 0 0 0 240 0 0 0

5.6.4 Performance level

The classification of performance level is performed based on a combination of the time-history-

and pushover analyses, with the governing factor being the interstory drift acceptance criteria. As

the structure is classified as a wall equivalent system, the performance of the beam- and column

hinges performs very well in all load cases. This means that the shear walls are expected to take

the most damage. As SAP2000 does not have the ability to directly determine the plastic hinge

rotation of the shear walls is not thoroughly determined.

Table 5-43 - Performance assessment according to time-history analysis

Operational

(O)

Immediate

Occupancy

(IO)

Life Safety

(LS)

Near Collapse

(NC)

50% / 50 years

10% / 50 years

2% / 50 years



6 DISCUSSION

6.1 Uncertainties in modelling and analysis

“Engineering is the art of modelling materials we do not wholly understand, into shapes we cannot

precisely analyze so as to withstand forces we cannot properly assess, in such a way that the public

has no reason to suspect the extent of our ignorance” – Dr. A.R. Dykes.

In the structural analysis process a number of assumptions and simplifications are performed to

get to the end results. It is therefore important to know where these were made, and what impact

this might have on the end results. This chapter will highlight the main assumptions and

simplifications made in the case study.

6.1.1 Structural analysis model

6.1.1.1 Meshing of shear walls:

The refinement of the mesh of the shear wall elements turned out to be a sensitive point of the

analysis model. A more refined mesh yielded a more torsional rigid analysis model and would

more realistically model the interaction between the shear wall and the beams. This in-part

decreased the computational efficiency drastically. It was therefore chosen to use the refined mesh

for linear-elastic analysis, while using the default meshing for nonlinear analysis. This should yield

more conservative results for the nonlinear analyses.

6.1.1.2 Constraints and SSI:

Soil-structure interaction is not required for the soil condition on this building site and is thereby

not included in this analytical model. The constraints are then considered as rigid, as all columns

are connected through should result in more conservative results, as when SSI is considered for

relatively stiff soils the soil is expected to sustain some of the energy from the earthquake.

6.1.1.3 Linear analysis model

For the linear analysis model all section was applied modification to account for the stiffness of

cracked concrete.

6.1.1.4 Modification for nonlinear analysis

For the shear walls, the software used did not have the capabilities of modelling plastic hinges in

shell elements. This means that plastic hinge formation in the shear walls is not properly captured

by the software used.

In the pushover analysis model automatic M3-hinges following ASCE 41-13 were used for

modelling nonlinear behavior in beams. For all other analysis, P-M2-M3 fiber hinges were used.

These are considered to provide the best representation of lumped nonlinear behavior, but there

lies some uncertainty on the assigned location of these hinges. All elements were assumed to have

a flexural failure mode, and the influence of shear forces is therefore not directly accounted for.



6.1.2 Analysis

6.1.2.1 Response Spectrum

All response spectrum analyses were performed using CQC modal combination. Although this

was not required by either code, it is widely considered as a more accurate approach as it considers

damping and the interaction of closely spaced modes.

6.1.2.2 Pushover

For the results of the pushover analysis it is important to note that the building is irregular in plan

and has big torsional contribution in its first modes. The real seismic behavior of the structure

might therefore not follow the same evolution as the pushover analysis indicates. This is a known

limitation to the N2 pushover procedure recommended by the Eurocode.

Other procedures have been proposed which include torsional effects, but these are much more

complicated. With the main advantages of the N2-pushover procedure being its efficiency and

relatively low complexity, the step in complexity towards the more accurate nonlinear time

analysis might not be much greater than the added complexity of a modal pushover analysis.

In the determination of the target displacements there is performed a bi-linearization of the

pushover curve, based on the displacement of plastic mechanism. In the Eurocode there are no

guidelines for determining this plastic mechanism. Although it might not have a significant impact,

it is an added uncertainty.

The design parameters obtained from the target displacements of the pushover analysis should

therefore not be used as a single source of structural design parameters. They do though make a

reasonable prediction of the overall performance level of the core building, and with a much more

efficient analysis process, compared to time-history analysis approaches.

The analysis was used to obtain the over-strength factor to modify the behavior factor, as the

margin from the calculated value to the maximum value allowed by the code was so significant.

6.1.2.3 Time-history

Non-linear time history is complex tool for seismic analysis. When performed right, it is

considered the most accurate analysis method, but there are many pitfalls along the way. In the

Eurocode, very few criteria are presented, so the output of the procedure is very much dependent

on the structural engineer. The uncertainties in such analysis are:

• Criteria for selection of ground motions

• Scaling and processing of ground motions

• Hinge- type and properties

• Assumed locations of plastic hinges

• Acceptance criteria for hinge rotation

• Choice of analysis form; direct integration- or modal time history

• Time integration algorithm

• Damping ratio

Both the benefits and limitations of the FNA- modal time history analysis, available in SAP200,

are exemplified in the case study of this thesis. The pros of the FNA method is its computational

efficiency and the consistency in evaluating of ground motions.



The direct integration analysis performed in this case study were very computational expensive,

with computing times between 10-24 hours per analysis for the case study. Direct integration

interpretation of ground motions is more sensitive to noise and errors in the ground motion signals.

In the case study, the results from direct integration time history analysis had a much greater

variability than that of modal time-history analysis. This could indicate that the ground motion

was not sufficiently processed.

The main difference of the procedures is the way the non-linear hinges are idealized. When direct

integration, and hinges are modeled within the structural elements, it can be seen that the full

expected behavior of a non-linear hinge is captured. As the earthquake progresses, the cyclic

degradation effect results in substantial increase in hinge rotation with similar bending moments.

For the FNA-model, the fiber hinge does show some non-linear behavior with the loading and

unloading of the hinge. The cyclic degradation seems though not be present, resulting in a

substantial underestimation of hinge rotation, which in-part affects the deflections of the building.

Figure 6-1 - Comparison of fiber-hinge result. L.S Direct integration, R.S. FNA

6.1.3 Results

6.1.3.1 Inter-story drifts

The inter-story drifts were evaluated at gravity center and corner of the stairway. These were

chosen to represent the overall behavior of the main structure and the stairway. There is through a

possibility that other parts of the structure do experience drifts. A vertical line of special interest

could be the elevator shaft. This could be further used to assess the performance and operationality

of the elevator.

6.1.3.2 Hinge rotations

Plastic hinges are modelled using M3 hinges following ASCE 41-13 and P-M2-M3 fiber hinges.

Both hinge models used does not account the effect of shear, as the failure mode is assumed to be

contributed by flexure. For beams the effect of shear, and for columns the axial force, is

incorporated into the acceptance criteria.

In the pushover analyses hinges were assigned to all beams and columns. For all the performance

levels there was no nonlinear behavior in the secondary beams. In the time-history analyses it was

therefore chosen to not include hinges in secondary beams to improve computational efficiency.

As



M3 hinges:

M3 hinges were for modelling nonlinear behavior in beams in the pushover analyses. Hinge

properties were set automatically after ASCE 41-13. These hinges allow the possibility of

assigning hinge rotation acceptance criteria in the program, allowing for graphically interpretation

of performance level. This simplifies the performance process substantially.

Fiber hinges:

Fiber hinges are the easiest to set up in SAP2000, as the hinge properties are set automatically

depending on the section properties.

In the pushover analyses, fiber hinges were used to model the nonlinear behavior of the columns.

The main reason behind this choice was the automatic P-M2-M3 hinges after ASCE 41-13 led to

convergence errors and the full behavior of the structure was not captured. When using P-M2-M3

fiber hinges, the analysis.

In the time-history analysis, the processing of the hinge results was very computationally

expensive. Retrieving all hinge results for one analysis took between 3-12 hours, depending on the

output steps.

6.1.3.3 Shear wall performance

The performance of the shear walls was determined solely by inter-story drifts. This was in-part

due to the fact that the analysis software did not have the capability to model nonlinear hinges in

shell elements.

6.2 Code comparison

This subchapter will highlight the main differences of Eurocode 8 and IS1893.


The peak ground motions used in the case study was based on a probabilistic seismic hazard

analysis [7] for the Kathmandu valley. This report indicates a PGA much higher than what is

presented in IS1893. This then raises the question of the applicability of the seismic zoning factors

prescribed in IS1893 and NBC105.

Figure 6-2 - Comparison of design seismic hazard for Kathmandu, Nepal



When comparing these design seismic hazards with the spectral response of the 2015 Gorkha

earthquake it is shown that the seismic demand of the earthquake is higher than what the code

requires for periods of 0.2s to 0.5s. This is problematic as buildings with code sufficient structural

design will have a high probability of being subjected to an even larger seismic demand within its

life-span, based on the recent history of earthquakes of high magnitudes (see Table 2-3).

The PGA-values used were further verified with the comparability of the responses of the linear

analysis with 50% probability of occurrence in 50years with the direct integration analysis of the

2015 Gorkha earthquake. Historically, there have been two earthquakes with this magnitude in the

last century (Table 2-3 - Earthquakes (>6.5Mw) in Nepal in the last century (From NCEI ), which

further strengthen this claim


Both codes require the use of effective (cracked concrete) stiffness in the analysis model. There

are here only minor differences between the two codes. Neither of the does though require a

reduction of torsional stiffness, but it was included in the case study as it was recommended in the

book Seismic Design of Concrete Buildings to Eurocode 8 [18].

Table 6-1 – Effective stiffness to model cracked moment of inertia

Beam Columns

Eurocode 8 50% 50%

IS1893 35% 70%

While the Eurocode has clear guidelines for the analysis model (planar or spatial), see Table 4-3,

IS1893 requires in clause 7.7.2 requires that irregularities are to be represented in the analysis

model. IS1893 therefore relies upon the judgement of the engineer for the use of analysis model.

6.2.3 Ground types

With IS1893 as a basis, the comparative ground types for NBC105 and Eurocode 8 is presented.

The main difference is for the classification of high-stiffness/bedrock ground types.

Table 6-2 - Comparison of ground types

IS1893 NBC 105 Eurocode 8 SPT-Value

Type 1 Type 1

Type A -

Type B >50

Type C 30-50

Type 2 Type 2 10-30

Type 3 Type 3 Type D <10


Eurocode 8 and IS1893 has a slightly different approach to the behavior factors. The Eurocode

sets an initial behavior factor depending on structural- and ductility classification, for then to



modify it depending on a number of factors (presented in Table 6-3 - Comparison of behavior

factor for Eurocode 8 and IS1893). After IS1893 the behavior factor is based solely on the

structural- and ductility classification, and no further modifications are allowed.

Table 6-3 - Comparison of behavior factor for Eurocode 8 and IS1893

Eurocode 8 IS1893

Ductility class DCL, DCM, DCH OMRF, SMRF, ductile shear walls

Torsional irregularity Reduced value Not allowed

Plan irregularity Decreased multiplication

factor

No effect

Vertical irregularity 20% reduced value No effect

Multiplication factor

dependent on structural

system

Up to 50% increased value Not allowed

Modification through

pushover analysis

Increased/decreased value Not allowed

Modification through

quality assurance

Max 20% increase Not allowed

While the Eurocode allows for higher behavior factors, the additional criteria set for the structural

system makes it harder to obtain a high behavior factor. For IS1893 there are fewer criteria to

obtain a medium-high behavior factor, but less room for modification and stricter regulations for

torsional irregularity. In-fact, IS1893 does not allow for torsional irregular structures.



6.3 Case Study

Through the analysis, the weakest points of the structural design were discovered. The most

prominent weakness is the stairway. This is due to the combined effect of irregularity in plan,

discontinuity in floor diaphragms, and short columns due to repose in the stairs.

The stairway can also be considered crucial in the evaluation of operationality of the hospital in

the case of larger earthquakes, as it would both hinder the access of floor 2-4 and, in the event of

collapse, hinder the main entrance to the building.

6.3.1 Comparison of code-compliant design forces

As discussed in chapter 6.2.1, the seismic demand differs significantly between Eurocode 8 and

IS1893. While IS1893 includes the conservative measure of scaling the response spectrum analysis

to match the base shears of the lateral force method, the difference in seismic demand is still large:

Table 6-4 - Comparison of code-compliant design forces

Later force method Response spectrum

IS1893 Eurocode 8 Difference IS1893 Eurocode 8 Difference

Base shear X [kN] 3 932 10 965 278% 3 965 8 876 224%

Base shear Y [kN] 3 932 10 965 278% 4 093 7 636 186%

As the approach to determining the interstory drifts differ between the codes, the interstory drifts

of IS1893 is multiplied by a factor of 5 (R – Behavior factor) as in Eurocode to compare the results:

Figure 6-3 - Comparison of inter-story drifts - Response spectrum anlysis



6.3.2 Eurocode 8

With regards to code compliance of Eurocode 8, the main problem is the difference in seismic

hazard (as discussed in chapter 6.2.1) consider in the code limit state. The structural design

originally is design after IS1839, with a seismic demand approximately half of the seismic demand

of the Eurocode (using PGA from source [23]). This resulted in the Damage limitation criteria not

being met for interstory drifts in the stairway. There is not performed member verification after

Eurocode 2, but from the performance assessment for seismic hazard of 2% probability of

occurrence in 50 years (2475-year return period, Table 4-1) it is suggested that the stairway will

be near the collapse limit.

As there was conduct both linear analysis, including behavior factors, and nonlinear analyses with

no reduction in seismic hazard, the results are compared separately:

6.3.2.1 Comparison of analysis results

All linear elastic load cases have the seismic weight included:

Table 6-5 - Comparison of base reactions for linear elastic analyses - EC8

L.F. - X L.F. - Y R.S. - X R.S. - Y R.S. - Z Linear Modal TH

Base shear X [kN] 10 965 3 289 8 876 7 636 3 548 12 018

Base shear Y [kN] 3 289 10 965 3 212 3 539 2 789 10 848

Base force Z [kN] 29 469 29 469 33 163 33 163 40 403 32 839

Mx [MNm] 373 459 407 456 481 463

My [MNm] 406 320 416 356 423 419

Mz [MNm] 100 71 118 138 68 165

For the nonlinear procedures, pushover- and time-history analyses were performed. As the seismic

hazard for the case study approximates the performance assessment time history with 2%

probability of occurrence in 50 years, these results are presented:

Table 6-6 - Comparison of base reactions for nonlinear analyses - EC8

Pushover X Pushover Y Direct integration TH

Base shear X [kN] 39 180 0 24188

Base shear Y [kN] 0 37 842 23279

Base force Z [kN] 29 469 29 469 46373

Mx [MNm] 338 672 795

My [MNm] 646 283 544

Mz [MNm] 446 365 343

6.3.3 IS1893

The initial structural design is designed after IS1893-2002 and is assumed to be sufficiently

modelled at member level for IS1893-2016. Through the analysis, two criteria’s regarding

regularity was found to non-compliant:

Table 6-7 - Non-compliant criteria - IS1893

Clause Criteria Comment



7.1 – Table 5 (i) Torsional irregularity Structure is considered torsional irregular,

which is not permitted for seismic zone V.

7.1 – Table 6 (vii) Irregular modes of oscillation in

two principal plan directions

The first three modes contribute less than

65% mass participation in principle plan

directions.

With regards to the seismic demand calculated after IS1893, there are questions to be raised

regarding the applicability of the zoning factors and return period of evaluation. This is further

discussed in chapter 6.2.1, and recommendation for further projects are given in chapter 7.

L.F. – X – EC8 L.F. – X – IS1893 Dif. % R.S. – X – EC8 R.S. – X – IS1893 Dif. %

Base shear X [kN] 10 965 3 932 179% 8 876 3 965 124%

Base shear Y [kN] 3 289 1 192 176% 3 212 1 559 101%

Base force Z [kN] 29 469 29 469 - 33 163 29 996 11%

Mx [MNm] 373 351 6% 407 358 14%

My [MNm] 406 335 21% 416 223 87%

Mz [MNm] 100 36 178% 118 55 115%

6.3.4 Seismic performance assessment

The seismic performance assessment was made on the basis of pushover analysis and time-history

analyses. To assess the performance, acceptance criteria was established for interstory drift and

for plastic hinge rotations for beams and columns. The interstory drift limits were set to account

for the performance of a wall-equivalent system and was assumed to be sufficient to assess the

performance of the shear walls. This was done as the software did not have the capability of

assigning nonlinear hinges to shell elements, and other procedures examined were too complicated

with regards to the time available. This is then considered as the greatest weakness of this seismic

performance assessment.

The seismic performance related to the different seismic hazard levels, as well as expected

damages are further discussed:

6.3.4.1 50% in 50 years

For the performance assessment for earthquakes of 50% probability of occurrence in 50 year, the

results from the pushover- and linear modal time history analysis were used. For the time-history

analysis the full suite of seven ground motions were used, so the mean results from this analysis

is used. From the pushover analysis it was evaluated that the structure would behave solely

linearly, with all hinges being classified as Operational as well as the interstory drifts being well

within the demand. With this in mind, it was assumed that it would be sufficient to perform a linear

modal time-history analysis.

As the time-history analyses does a better job of representing the real behavior of the structure, it

was the guiding analysis for the performance assessment.

The structure was classified right at the limit of Immediate Occupancy. This was due to the

interstory drift of the stairway. The following expectations are made for an earthquake of this

magnitude:



• The stairway might endure some damage which will most likely be related to the infill

walls, and not the structural system (columns and beams).

• The core building will, according to the analysis, not endure any significant damage and

will be operational.

6.3.4.2 10% in 50 years


results from the pushover- and nonlinear direct integration time-history analysis were used. For

the time-history analysis a suite of three ground motions were used (Cape Mendocino, Iwate and

Northridge), so the least favorable results were used.

Again the, time-history analysis was the governing factor in the performance assessment. The

results for the core building was though very similar.

The structure was classified as being right at the limit of Life Safety. The following expectations

are made for an earthquake of this magnitude:

• The stairway might endure significant damage in the infill walls, and columns and beams

will endure some damage and permanent deformations.

• The core building will, according to the analysis, not endure any significant damage and

will be operational.

6.3.4.3 2% in 50 years


results from the pushover- and nonlinear direct integration time-history analysis were used. For

the time-history analysis the full suite of seven ground motions were used, so the mean values

were used.

The structure was classified as being right at the limit of Collapse prevention. The following

expectations are made for an earthquake of this magnitude:

• In the stairway infill walls may collapse and significant damage is to be expected for beams

and columns.

• The core building is classified as Immediate Occupancy. Larger damage is expected for

nonstructural components, such as dividing walls and ceiling finishing, while the beams

and columns will have minor permanent deformations. This results in the core building

being habitable but not necessarily operational.

6.3.5 Measures to improve performance level

As noted throughout the case study, the stairway is considered the weakest point of the structural

system and is the governing factor for all performance assessments. This should therefore be the

main focus when considering measures to improve the seismic performance. The underlying

problem is the torsional irregularity the stairway poses, and so the measures should focus on

deceasing the torsional irregularity. This can be measured by checking the modal mass



participation for the selected measures. For the original linear-elastic analysis model has the

following modal mass participation are found the horizontal- and torsion rotational direction:

Table 6-8 - Modal mass participation ratio - Linear elastic analysis model

Modal mass participation ratio

Mode Period [s] Ux Uy Rz

1 0.43 0% 46% 23%

2 0.33 61% 0% 4%

3 0.30 0% 22% 30%

4 0.22 7% 0% 10%

The best measure to improve the seismic performance would be to reconfigure the plan

configuration to satisfy the criteria of regularity in plan. As this would have great impact on the

progress of the project, some measures with a lower impact is further discussed:

6.3.5.1 Slanted roof in stairway

As the largest interstory drifts occur at the top of the stairway tower, a possible solution is to reduce

the height. With the slanted roof extending from the beam of the terrace level to the top of the

stairway, the minimum height in the stairway would be 1.8m. This is on the low-side, but might

be permissible if the roof is not intended for large activity.

Figure 6-4 - Proposed design change - slanted roof in stairway



The following results are obtained from a modal analysis:

Modal mass

participation ratio

Change in

modal mass

participation

Mode Period [s] Ux Uy Rz ∆Ux ∆Uy ∆Rz

1 0.42 0% 49% 23% 0% 3% 0%

2 0.33 62% 0% 7% 1% 0 3%

3 0.28 7% 22% 39% 7% 0 9%

4 0.19 0% 0% 0% -7% 0 -10%

This measure increases the modal mass participation slightly in the horizontal directions. The

increase is enough to satisfy the demand in IS1893 of 65% modal mass participation in horizontal

directions for the first three modes of vibration.

6.3.5.2 Extend elevator shaft to top of building

To improve the torsional stiffness of the stairway roof, the shear walls of the elevator shaft could

be extended to the roof.

Figure 6-5 - Proposed design change - extend elevator shaft to stairway-roof

Modal mass

participation ratio

Change in

modal mass

participation

Mode Period [s] Ux Uy Rz ∆Ux ∆Uy ∆Rz

1 0.43 0.3% 48% 23% 0.3% 2% 0%

2 0.33 62% 1% 7% 1% 1% 3%

3 0.28 7% 23% 39% 7% 1% 9%

4 0.19 0% 0% 0% -7% 0% -10%



This measure increases the modal mass participation slightly in the horizontal directions. The

increase is enough to satisfy the demand in IS1893 of 65% modal mass participation in horizontal

directions for the first three modes of vibration.

6.3.5.3 Increase rebar in stairway columns

In the nonlinear time history analyses with 2% probability of occurrence in 50 years, the axial

impact on the stairway columns was significantly higher than what the other analyses suspected.

Increasing the amount of rebar in the columns of the stairway will not greatly affect the torsional

rigidity of the overall structure. It will though improve the capacity of the columns, and thereby

increasing the performance of the stairway.



7 CONCLUSION

The case study of this thesis had three purposes; to determine if the structure is code compliant

after IS1893, to determine how this compares to seismic design after Eurocode 8, and lastly to

determine the true structural performance for earthquakes of 50%- 10%- and 2%- probability of

occurrence in 50 years. There was also performed analyses using ground motions from the 2015

Gorkha earthquake, which was found to have a seismic hazard equivalent of the 50%/50years

hazard level.

The following conclusion are made:

• The structure is considered to partly code compliant to IS1893, with one limitation. The

structure is considered to be torsional irregular, which is not allowed by the code. To

comply with this demand there needs to be a change to increase the torsional stiffness or

reduce the torsional radius of the building.

• The structure is not compliant to Eurocode 8. This is mostly due to the difference in seismic

demands, which for the Eurocode analysis is based on PGA’s from a PSHA [9]. Though

the structure is not expected to collapse, it is expected to sustain more damage than what

is considered acceptable by the code.

• The structural performance was evaluated after FEMA 356 and ASCE 41-13 to be the

following:

Table 7-1 - Performance level of Kanti Children’s hospital

Operational

(O)

Immediate

Occupancy

(IO)

Life Safety

(LS)

Near Collapse

(NC)

50% / 50 years*

10% / 50 years

2% / 50 years

* equivalent to the 2015 Gorkha earthquake.

The stairway is identified as the weakest spot of the building and is governing the performance

assessment. The following proposals are med to improve the structural performance of the

building, and are arranged from least- to most-impacting:

• Increase amount of rebar in column B-5 and C-5 (Stairway)

• Recalculate the whole structural system with a higher zone factor. From the PSHA for

Kathmandu it is suggested to use a zone factor of Z=0.49g.

• Relocate, add, and/or extend shear walls to reduce torsional irregularity.

• Reduce the height of the stairway tower.

• Architectural redesign to incorporate the stairway into the main building and reducing the

irregularity in plan.

For further projects in Nepal, seismic prone regions, the following recommendations are made for

the contractors or subsidiaries involved in the project, to ensure good seismic performance:

• Ensure that the seismic demand set for the building is reasonable with regards to PSHA for

the project site.

• Specify, and value, structural regularity in preliminary design phase.

• Specify the wanted performance level for the structure for different earthquake scenarios.



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Appendix A – Architectural drawings of Kanti Children’s hospital

Architectural drawings by Monika Shrestha at TEAM Consultants.

X-axis

Y-a

xis





Appendix B – Flowcharts

B-1: Linear elastic analysis flowchart



B-2: Pushover analysis flowchart



B-3: Time-history analysis flowchart



Appendix C – N2-Pushover Procedure C-1: Eurocode 8:



















C-2: Performance assessment using N2-Pushover procedure

















Appendix D – Analysis Results D-1:Linear Modal Time History – 50% probability in 50 years


Base reactions 95

Base shear X [kN] 13870 10041 9732 13761 12061 12671 11991 12018

Base shear Y [kN] 9867 13214 9143 10625 9834 9697 13553 10848

Base force Z [kN] 31519 32845 31949 35062 31376 32319 34804 32839

Mx [MNm] 440 498 417 474 455 459 495 463

My [MNm] 448 396 415 423 414 419 419 419

Mz [MNm] 135 196 122 217 170 129 188 165

Interstory drift gravity

X Y Tr X Y Tr X Y Tr X Y Tr X Y Tr X Y Tr X Y Tr X Y Tr

Base 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

Story 2 0.06% 0.05% 0.06% 0.05% 0.07% 0.07% 0.05% 0.06% 0.07% 0.06% 0.07% 0.08% 0.05% 0.07% 0.07% 0.06% 0.06% 0.07% 0.05% 0.09% 0.09% 0.06% 0.07% 0.07%

Story 3 0.12% 0.10% 0.13% 0.11% 0.13% 0.15% 0.11% 0.13% 0.14% 0.13% 0.15% 0.16% 0.11% 0.15% 0.15% 0.12% 0.13% 0.14% 0.11% 0.18% 0.18% 0.12% 0.14% 0.15%

Story 4 0.15% 0.12% 0.16% 0.14% 0.15% 0.17% 0.14% 0.16% 0.17% 0.16% 0.18% 0.19% 0.14% 0.18% 0.18% 0.15% 0.16% 0.18% 0.14% 0.22% 0.22% 0.14% 0.17% 0.18%

Roof 0.16% 0.12% 0.16% 0.14% 0.15% 0.17% 0.15% 0.17% 0.18% 0.17% 0.19% 0.20% 0.15% 0.19% 0.19% 0.16% 0.17% 0.18% 0.14% 0.22% 0.22% 0.15% 0.17% 0.19%

Interstory drift stairway


Base 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

Story 2 0.08% 0.04% 0.08% 0.10% 0.06% 0.10% 0.08% 0.04% 0.08% 0.12% 0.08% 0.14% 0.09% 0.06% 0.10% 0.11% 0.07% 0.11% 0.17% 0.10% 0.18% 0.11% 0.07% 0.11%

Story 3 0.13% 0.07% 0.14% 0.18% 0.11% 0.18% 0.15% 0.08% 0.15% 0.23% 0.15% 0.24% 0.16% 0.11% 0.18% 0.18% 0.13% 0.18% 0.27% 0.17% 0.29% 0.19% 0.12% 0.19%

Story 4 0.16% 0.08% 0.16% 0.22% 0.13% 0.22% 0.19% 0.09% 0.19% 0.29% 0.18% 0.29% 0.18% 0.13% 0.21% 0.21% 0.15% 0.23% 0.31% 0.20% 0.34% 0.22% 0.14% 0.23%

Roof 0.35% 0.08% 0.35% 0.45% 0.14% 0.45% 0.35% 0.09% 0.35% 0.59% 0.19% 0.59% 0.33% 0.13% 0.33% 0.42% 0.16% 0.43% 0.54% 0.20% 0.54% 0.43% 0.14% 0.44%

Mumty 0.44% 0.17% 0.45% 0.54% 0.25% 0.55% 0.42% 0.18% 0.43% 0.72% 0.30% 0.73% 0.41% 0.19% 0.41% 0.52% 0.27% 0.53% 0.63% 0.30% 0.63% 0.53% 0.24% 0.53%







D-2:Nonlinear Modal Time History Analysis – 10% probability in 50 years


Base reactions 10% probability in 50 years

Base shear X [kN] 23082 23246 20234 21554 20353 21468 17745 21097

Base shear Y [kN] 17867 18980 16877 20134 22178 21107 22999 20020

Base force Z [kN] 33746 35934 33733 39644 32489 34690 38761 35571

Mx [MNm] 505 558 542 548 566 587 515 546

My [MNm] 475 490 517 517 499 517 467 497

Mz [MNm] 281 285 253 260 291 292 358 289

Interstory drift gravity center 10% probability in 50 years


Base 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

Story 2 0.03% 0.04% 0.04% 0.03% 0.04% 0.04% 0.03% 0.04% 0.04% 0.03% 0.05% 0.05% 0.03% 0.05% 0.05% 0.03% 0.05% 0.05% 0.03% 0.05% 0.05% 0.03% 0.05% 0.05%

Story 3 0.11% 0.13% 0.13% 0.12% 0.13% 0.13% 0.12% 0.12% 0.13% 0.11% 0.14% 0.15% 0.09% 0.15% 0.16% 0.10% 0.15% 0.15% 0.09% 0.15% 0.16% 0.11% 0.14% 0.14%

Story 4 0.10% 0.17% 0.18% 0.16% 0.16% 0.17% 0.16% 0.15% 0.17% 0.14% 0.19% 0.19% 0.12% 0.20% 0.20% 0.13% 0.19% 0.19% 0.12% 0.19% 0.21% 0.13% 0.18% 0.19%

Roof 0.15% 0.18% 0.19% 0.17% 0.17% 0.19% 0.17% 0.16% 0.18% 0.15% 0.19% 0.20% 0.12% 0.21% 0.21% 0.14% 0.20% 0.20% 0.13% 0.20% 0.21% 0.15% 0.19% 0.20%

Interstory drift stairway 10% probability in 50 years


Base 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

Story 2 0.08% 0.04% 0.08% 0.07% 0.04% 0.08% 0.08% 0.03% 0.08% 0.07% 0.04% 0.07% 0.09% 0.04% 0.09% 0.08% 0.04% 0.08% 0.08% 0.05% 0.08% 0.08% 0.04% 0.08%

Story 3 0.16% 0.09% 0.18% 0.16% 0.10% 0.17% 0.14% 0.09% 0.15% 0.13% 0.10% 0.14% 0.14% 0.09% 0.14% 0.16% 0.11% 0.16% 0.14% 0.12% 0.17% 0.15% 0.10% 0.16%

Story 4 0.21% 0.13% 0.22% 0.21% 0.14% 0.22% 0.18% 0.13% 0.18% 0.17% 0.13% 0.17% 0.18% 0.12% 0.18% 0.21% 0.14% 0.22% 0.18% 0.15% 0.21% 0.19% 0.13% 0.20%

Roof 0.78% 0.13% 0.78% 0.72% 0.15% 0.72% 0.72% 0.14% 0.72% 0.61% 0.15% 0.61% 0.68% 0.13% 0.68% 0.72% 0.16% 0.72% 0.72% 0.17% 0.62% 0.71% 0.15% 0.69%

Mumty 1.17% 0.38% 1.19% 1.08% 0.42% 1.09% 1.08% 0.50% 1.08% 0.89% 0.44% 0.90% 0.97% 0.35% 0.98% 1.03% 0.45% 1.03% 0.85% 0.34% 0.86% 1.01% 0.41% 1.02%







D-3: Nonlinear Modal Time History Analysis – 2% probability in 50 years Cape Mendocino Iwate Chuetsu SMART1 Chichi Northridge Loma Prieta Mean

Base reactions 2% probability in 50 years

Base shear X [kN] 34532 32321 29478 30890 33808 31892 26851 31396

Base shear Y [kN] 27505 26353 24430 29609 32527 31170 33586 29311

Base force Z [kN] 32550 38839 35787 44053 33807 37104 43281 37917

Mx [MNm] 599 646 635 646 671 706 516 631

My [MNm] 557 683 623 617 598 632 554 609

Mz [MNm] 407 351 366 381 425 415 529 411

Interstory drift gravity center 2% probability in 50 years X Y Tr X Y Tr X Y Tr X Y Tr X Y Tr X Y Tr X Y Tr X Y Tr

Base 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

Story 2 0.05% 0.06% 0.06% 0.05% 0.06% 0.06% 0.05% 0.05% 0.06% 0.04% 0.07% 0.07% 0.03% 0.08% 0.08% 0.04% 0.07% 0.07% 0.04% 0.07% 0.08% 0.04% 0.07% 0.07%

Story 3 0.17% 0.19% 0.20% 0.17% 0.17% 0.18% 0.17% 0.17% 0.18% 0.16% 0.21% 0.21% 0.09% 0.23% 0.23% 0.15% 0.22% 0.22% 0.13% 0.22% 0.24% 0.15% 0.20% 0.21%

Story 4 0.22% 0.25% 0.27% 0.22% 0.23% 0.24% 0.23% 0.23% 0.24% 0.21% 0.28% 0.28% 0.12% 0.29% 0.30% 0.20% 0.28% 0.29% 0.18% 0.28% 0.30% 0.20% 0.26% 0.27%

Roof 0.23% 0.26% 0.28% 0.23% 0.24% 0.25% 0.24% 0.24% 0.25% 0.22% 0.29% 0.29% 0.13% 0.31% 0.31% 0.21% 0.30% 0.30% 0.18% 0.29% 0.32% 0.21% 0.28% 0.29%

Interstory drift stairway 2% probability in 50 years X Y Tr X Y Tr X Y Tr X Y Tr X Y Tr X Y Tr X Y Tr X Y Tr

Base 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

Story 2 0.11% 0.06% 0.12% 0.10% 0.05% 0.10% 0.12% 0.05% 0.12% 0.10% 0.05% 0.11% 0.13% 0.06% 0.13% 0.11% 0.06% 0.11% 0.11% 0.07% 0.12% 0.11% 0.06% 0.11%

Story 3 0.24% 0.14% 0.26% 0.21% 0.13% 0.22% 0.21% 0.13% 0.21% 0.18% 0.14% 0.20% 0.20% 0.14% 0.21% 0.23% 0.16% 0.23% 0.20% 0.18% 0.25% 0.21% 0.15% 0.23%

Story 4 0.30% 0.20% 0.32% 0.28% 0.18% 0.29% 0.26% 0.20% 0.26% 0.23% 0.19% 0.25% 0.26% 0.18% 0.27% 0.31% 0.21% 0.31% 0.25% 0.22% 0.32% 0.27% 0.20% 0.29%

Roof 1.16% 0.20% 1.16% 1.04% 0.19% 1.04% 1.10% 0.21% 1.10% 0.96% 0.22% 0.96% 1.01% 0.19% 1.01% 1.09% 0.23% 1.09% 0.94% 0.25% 0.94% 1.04% 0.21% 1.04%

Mumty 1.83% 0.60% 1.85% 1.32% 0.56% 1.36% 1.73% 0.78% 1.73% 1.46% 0.66% 1.47% 1.46% 0.52% 1.48% 1.57% 0.68% 1.57% 1.31% 0.52% 1.33% 1.52% 0.62% 1.54%







D-4:Nonlinear Direct Integration Time History – 10% probability in 50 years

Table 7-2 - Results from direct integration analysis with 10% probability of occurrence in 50 years

Cape Mendocino Iwate Northridge Least favorable

Base reactions 10% in 50years

Base shear X [kN] 13579 21571 16725 21571

Base shear Y [kN] 15987 23285 13845 23285

Base force Z [kN] 36167 30822 35983 36167

Mx [MNm] 555 574 515 574

My [MNm] 466 497 474 497

Mz [MNm] 200 304 188 304

Interstory drift gravity center 10% in 50 years

X Y Trans X Y Trans X Y Trans X Y Trans

Base 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

Story 2 0.10% 0.15% 0.15% 0.16% 0.20% 0.20% 0.12% 0.12% 0.13% 0.16% 0.20% 0.20%

Story 3 0.21% 0.30% 0.30% 0.30% 0.41% 0.41% 0.25% 0.25% 0.27% 0.30% 0.41% 0.41%

Story 4 0.25% 0.33% 0.33% 0.32% 0.47% 0.47% 0.29% 0.29% 0.32% 0.32% 0.47% 0.47%

Roof 0.26% 0.32% 0.32% 0.32% 0.46% 0.46% 0.29% 0.28% 0.32% 0.32% 0.46% 0.46%

Interstory drift stairway 10%in 50 years

X Y X Y X Y X Y Trans

Base 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

Story 2 0.13% 0.08% 0.15% 0.23% 0.15% 0.26% 0.15% 0.10% 0.15% 0.23% 0.15% 0.26%

Story 3 0.22% 0.14% 0.26% 0.40% 0.25% 0.44% 0.24% 0.19% 0.24% 0.40% 0.25% 0.44%

Story 4 0.25% 0.16% 0.29% 0.43% 0.28% 0.48% 0.27% 0.21% 0.27% 0.43% 0.28% 0.48%

Roof 0.47% 0.17% 0.48% 0.75% 0.30% 0.77% 0.58% 0.21% 0.58% 0.75% 0.30% 0.77%

Mumty 0.54% 0.30% 0.56% 0.97% 0.36% 0.97% 0.81% 0.38% 0.83% 0.97% 0.38% 0.97%



Figure 7-1 - Interstory drift at gravity center - 10% probability in 50 years

Figure 7-2 - Interstory drift at stairway - 10% probability in 50 years



D-5:Nonlinear Direct Integration Time History – 2% probability in 50 years


Base shear X [kN] 21875 29404 19289 28831 19288 19258 31369 24188

Base shear Y [kN] 22681 25279 22570 21484 22570 19145 29222 23279

Base force Z [kN] 39504 54942 40831 61336 40831 39209 47957 46373

Mx [MNm] 644 958 675 1142 675 623 845 795

My [MNm] 529 584 465 645 464 518 602 544

Mz [MNm] 271 361 300 518 304 247 400 343

Interstory drift – Gravity Center


Base 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

Story 2 0.17% 0.25% 0.25% 0.23% 0.20% 0.24% 0.12% 0.17% 0.17% 0.27% 0.23% 0.28% 0.12% 0.17% 0.17% 0.16% 0.19% 0.19% 0.27% 0.27% 0.27% 0.19% 0.21% 0.22%

Story 3 0.34% 0.50% 0.51% 0.45% 0.39% 0.46% 0.24% 0.34% 0.34% 0.59% 0.46% 0.60% 0.25% 0.34% 0.34% 0.33% 0.38% 0.39% 0.53% 0.53% 0.54% 0.39% 0.42% 0.45%

Story 4 0.40% 0.56% 0.56% 0.49% 0.43% 0.49% 0.29% 0.39% 0.39% 0.70% 0.51% 0.72% 0.30% 0.39% 0.39% 0.39% 0.43% 0.44% 0.58% 0.61% 0.62% 0.45% 0.48% 0.52%

Roof 0.41% 0.55% 0.55% 0.48% 0.42% 0.49% 0.31% 0.38% 0.39% 0.72% 0.51% 0.73% 0.31% 0.38% 0.39% 0.40% 0.43% 0.43% 0.56% 0.59% 0.61% 0.45% 0.47% 0.51%

Interstory drift – Stairway


Base 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%

Story 2 0.21% 0.20% 0.27% 0.29% 0.17% 0.29% 0.21% 0.15% 0.22% 0.39% 0.20% 0.41% 0.21% 0.15% 0.22% 0.23% 0.16% 0.23% 0.33% 0.21% 0.36% 0.27% 0.18% 0.29%

Story 3 0.35% 0.35% 0.48% 0.44% 0.28% 0.45% 0.33% 0.25% 0.35% 0.57% 0.37% 0.62% 0.33% 0.25% 0.35% 0.36% 0.30% 0.38% 0.50% 0.39% 0.59% 0.41% 0.31% 0.46%

Story 4 0.40% 0.42% 0.55% 0.48% 0.31% 0.48% 0.36% 0.29% 0.39% 0.63% 0.44% 0.69% 0.36% 0.29% 0.39% 0.40% 0.33% 0.42% 0.58% 0.43% 0.66% 0.46% 0.36% 0.51%

Roof 0.87% 0.43% 0.87% 0.66% 0.32% 0.66% 0.86% 0.31% 0.86% 1.11% 0.47% 1.14% 0.86% 0.31% 0.86% 0.82% 0.33% 0.82% 1.15% 0.44% 1.15% 0.90% 0.37% 0.91%

Mumty 1.31% 0.54% 1.32% 0.80% 0.51% 0.80% 1.29% 0.54% 1.32% 1.22% 0.73% 1.25% 1.29% 0.54% 1.32% 1.21% 0.56% 1.23% 1.72% 0.58% 1.72% 1.26% 0.57% 1.28%



Figure 7-3 - Interstory drift at gravity center - 2% probability in 50 years

Figure 7-4 - Interstory drift at stairway - 2% probability in 50 years



D-6: Gorkha Earthquake – Direct integration time history analysis

Gorkha Earthquake

Base shear X [kN] 9 863

Base shear Y [kN] 8 360

Base force Z [kN] 34 095

Mx [MNm] 410

My [MNm] 393

Mz [MNm] 140



D-7:Hinge Performance – 10% in 50 years

Hinge performance for beams and columns with performance level IO or lower:

Beam performance:

Pushover Nonlinear Direct Integration Time-History

Beam X-direction Y-direction Iwate Northridge Cape

Mendocino Least

favorable

B-5-4 – C-5-4 O O IO IO IO IO

D-1-2 – F-1-2 IO O O O O IO

F-1-1 – F-2-1 O O IO O O IO

F-1-2 – F-2-2 O IO IO O O IO

F-1-3 – F-2-3 O IO IO O O IO

F-1-4 – F-2-4 O IO IO O O IO

Column performance


Column X-direction Y-direction Iwate Northridge Cape

Mendocino

Least favorable

B-4-2 O O IO O O IO

C-1-4 O O O O O IO

D-1-2 O O O O O IO

D-1-4 IO O O O IO IO

F-2-2 O O IO O O IO

F-2-3 O O IO O O IO

F-2-4 O O IO O O IO

F-3-1 O O O O O IO



D-8:Hinge Performance – 2% in 50 years

Beam performance:


Beam X-direction Y-direction Iwate Northridge Cape Mendocino Chuetsu Loma Prieta Chi-chi Smart1 Least favorable

B-3-2 – B-4-2 O IO O O O O IO O IO IO

B-5-3.5 – C-5-3.5 O O IO IO IO IO IO IO IO IO

B-5-4 – C-5-4 IO O O IO IO IO LS IO IO LS

C-4-2 – C-5-2 O O O O O O IO O O IO

C-4-3 – C-5-3 O O O O O O IO O O IO

D-1-1 – F-1-1 IO O O O IO O O O IO IO

D-1-2 – F-1-2 IO O O IO IO O IO O LS LS

D-1-3 – F-1-3 IO O O IO IO O IO O LS IO

D-1-4 – F-1-4 IO O O IO IO O IO O LS IO

D-3-1 – F-3-1 IO O O O O O O O O IO

D-3-2 – F-3-2 IO O O O O O O O IO IO

E-3-3 – E-4-3 O IO O O O O O O O IO

E-3-4 – E-4-4 O IO O O O O O O O IO

F-1-1 – F-2-1 O IO O O IO O IO O IO IO

F-1-2 – F-2-2 O IO O IO IO IO IO IO IO IO

F-1-3 – F-2-3 O IO O IO IO IO IO IO IO IO

F-1-4 – F-2-4 O IO O O IO IO IO IO IO IO



Column performance:

Pushover Nonlinear Direct Integration Time History

Column X-direction Y-direction Iwate Northridge Cape Mendocino Chuetsu Loma Prieta Chi-chi Smart1 Least favorable

A-3-1 LS O O O O O O O O LS

B-4-2 O O IO IO IO O IO IO IO IO

B-4-4 O O O IO IO IO IO IO IO IO

B-5-0.5 O LS O O O O IO O IO LS

B-5-1 O O O O O O IO O IO IO

B-5-1.5 O LS O O O O IO O IO LS


B-5-2.5 O O O O O O IO O IO IO


B-5-3.5 O O O O O O IO O IO IO

B-5-4 O O O IO O O IO O NC NC

B-5-5 O O IO O O O IO O NC NC

C-1-4 IO O O O O O O O IO IO

C-2-4 O IO O O O O IO O IO IO

C-3-1 IO O O O O O O O O IO

C-4-2 O O O IO O IO IO IO IO IO

C-4-4 O O O IO IO IO IO IO IO IO

C-5-0.5 O LS O O O O IO O IO LS

C-5-1 O O O O O O IO O IO IO

C-5-1.5 O O O O O O IO O IO IO








C-5-5 O O IO O IO IO NC IO NC NC

D-1-1 O O O O O O IO O IO O

D-1-2 IO O O IO O O IO O IO IO

D-1-3 IO O O IO IO O IO O IO IO

D-1-4 IO IO IO IO IO IO IO IO IO IO

D-2-2 O LS O O O O O O IO LS

D-2-3 LS LS O O O O IO O IO LS

D-2-4 IO LS O O O O IO O IO LS

D-3-2 LS O IO O O O IO O IO LS

D-3-3 LS O IO O O O IO O IO LS

D-3-4 IO O IO IO IO O IO O IO IO

D-4-4 O IO O O O O IO O IO IO

E-4-4 O IO O O O O IO O IO IO

F-1-1 LS LS O O O O IO O IO LS

F-2-1 O IO O O O O IO O IO IO

F-2-2 O LS O IO IO IO IO IO IO LS

F-2-3 O LS O O IO IO IO IO IO LS

F-2-4 O LS IO IO IO IO IO IO IO LS

F-3-1 IO O O O O O O O O IO